Theory and Applications of Categories

ISSN 1201 - 561X

Foreword

The guest editors, 1-1 pdf

1. What is the universal property of the 2-category of monads?

Stephen Lack and Adrian Miranda, 2-18 abstract | pdf

2. Inner automorphisms as 2-cells

Pieter Hofstra and Martti Karvonen, 19-40 abstract | pdf

3. Topological endomorphism monoids of models of geometric theories

Morgan Rogers, 41-58 abstract | pdf

4. Quotients, pure existential completions and arithmetic universes

Maria Emilia Maietti and Davide Trotta, 59-83 abstract | pdf

5. Inner automorphisms of groupoids

Richard Garner, 84-101 abstract | pdf

6. Classical Distributive Restriction Categories

Robin Cockett and Jean-Simon Pacaud Lemay, 102-144 abstract | pdf

7. Factorization Systems for Restriction Categories

Robin Cockett, G.S.H. Cruttwell, Jonathan Gallagher, and Dorette Pronk, 145-171 abstract | pdf

8. The least subtopos containing the discrete skeleton of Ω

M. Menni, 172-179 abstract | pdf

9. The eventual image

Tom Leinster, 180-221 abstract | pdf

10. Weak vertical composition

Eugenia Cheng and Alexander S. Corner, 222-262 abstract | pdf

11. Internal parameterization of hyperconnected quotients

Ryuya Hora, 263-313 abstract | pdf

12. A syntactic characterization of weakly Mal'tsev varieties

Nadja Egner, Pierre-Alain Jacqmin, and Nelson Martins-Ferreira, 314-353 abstract | pdf

Foreword

The guest editors, 1-2 pdf

1. Monoidal centres and groupoid-graded categories

Branko Nikolić and Ross Street, 3-31 abstract | pdf

2. Normalizers in the non-pointed context

Dominique Bourn, 32-62 abstract | pdf

3. Cartesian Closed Double Categories

Susan Niefield, 63-79 abstract | pdf

4. Geometric morphisms between toposes of monoid actions: factorization systems

Jens Hemelaer and Morgan Rogers, 80-129 abstract | pdf

5. Retrocells

Robert Paré, 130-179 abstract | pdf

6. Lax comma 2-categories and admissible 2-functors

Maria Manuel Clementino and Fernando Lucatelli Nunes, 180-226 abstract | pdf

7. On the metrical and quantalic versions of the *-autonomous category of sup-lattices

Walter Tholen, 227-248 abstract | pdf

8. On coherent systems of subobjects with application to torsion theories

Francis Borceux and Maria Manuel Clementino, 249-277 abstract | pdf

9. Distributive idempotents in an order-enriched category

Christopher Townsend, 278-300 abstract | pdf

10. Birkhoff subfibrations of the codomain fibration

A. S. Cigoli and S. Mantovani, 301-323 abstract | pdf

11. Integration of 1-forms and connections

Anders Kock, 324-336 abstract | pdf

12. Duality for positive opetopes and positive zoom complexes

Marek Zawadowski, 337-370 abstract | pdf

13. A comonad for Grothendieck fibrations

Jacopo Emmenegger, Luca Mesiti, Giuseppe Rosolini, and Thomas Streicher, 371-389 abstract | pdf

14. The oplax limit of an enriched category

Soichiro Fujii and Stephen Lack, 390-412 abstract | pdf

15. Bi-directional models of `Radically Synthetic' Differential Geometry

Matías Menni, 413-429 abstract | pdf

16. KZ-pseudomonads and Kan injectivity

Ivan Di Liberti, Gabriele Lobbia, and Lurdes Sousa, 430-478 abstract | pdf

17. Higher coverings of racks and quandles - Part I

Fara Renaud, 479-536 abstract | pdf

18. The 2-localization of a model category

Dubuc E. J., Girabel J., 537-574 abstract | pdf

Postface: Remembrances of Marta Bunge

Silvia Bunge, Andrée Ehresmann, and Valeria de Paiva, 575-578 pdf

* The Editors of TAC wish to thank Maria Manuel Clementino, Valeria de Paiva, and Jonathon Funk who acted as guest editors for this special volume.

1. Action representability of the category of internal groupoids

Marino Gran and James Richard Andrew Gray, 1-13 abstract | pdf

2. On the formal theory of pseudomonads and pseudodistributive laws

Nicola Gambino and Gabriele Lobbia, 14-56 abstract | pdf

3. Yetter-Drinfel'd algebras and coideals of Weak Hopf C*-Algebras

Leonid Vainerman and Jean-Michel Vallin, 57-94 abstract | pdf

4. Ladders and completion of triangulated categories

Yongliang Sun and Yaohua Zhang, 95-106 abstract | pdf

5. Dependent products and 1-inaccessible universes

Giulio Lo Monaco, 107-143 abstract | pdf

6. (Co)ends for representations of tensor categories

Noelia Bortolussi and Martín Mombelli, 144-188 abstract | pdf

7. The Moore Complex of a Simplicial Cocommutative Hopf Algebra

Kadir Emir, 189-226 abstract | pdf

8. The 2-nerve of a 2-group and Deligne's determinant functors

Elhoim Sumano, 227-265 abstract | pdf

9. Remarks on combinatorial and accessible model categories

Jiri Rosický, 266-275 abstract | pdf

10. Simplicial sets inside cubical sets

Thomas Streicher and Jonathan Weinberger, 276-286 abstract | pdf

11. Pivotal objects in monoidal categories and their Hopf monads

Aryan Ghobadi, 287-325 abstract | pdf

12. A remarkable aspect of internal groupoids in regular Mal'tsev categories

Dominique Bourn, 326-336 abstract | pdf

13. Every elementary higher topos has a natural number object

Nima Rasekh, 337-377 abstract | pdf

14. A new approach to S-protomodular categories

Tamar Janelidze-Gray, 378-387 abstract | pdf

15. A closed model structure on the category of weakly unital dg categories, II

Piergiorgio Panero and Boris Shoikhet, 388-417 abstract | pdf

16. A homotopy theory of coherently commutative monoidal quasi-categories

Amit Sharma, 418-481 abstract | pdf

17. Parsummable categories as a strictification of symmetric monoidal categories

Tobias Lenz, 482-529 abstract | pdf

18. Descent data and absolute Kan extensions

Fernando Lucatelli Nunes, 530-561 abstract | pdf

19. Left properness of flows

Philippe Gaucher, 562-612 abstract | pdf

20. A Hurewicz model structure for directed topology

Sanjeevi Krishnan and Paige Randall North, 613-634 abstract | pdf

21. Tensor-restriction categories

Chris Heunen and Jean-Simon Pacaud Lemay, 635-670 abstract | pdf

22. Discrete Double Fibrations

Michael Lambert, 671-708 abstract | pdf

23. Coherent Nerves for Higher Quasicategories

Harry Gindi, 709-817 abstract | pdf

24. A categorical approach to quantum moment maps

Pavel Safronov, 818-862 abstract | pdf

25. A practical type theory for symmetric monoidal categories

Michael Shulman, 863-907 abstract | pdf

26. An Essential Local Geometric Morphism which is not Locally Connected though its Inverse Image Part is an Exponential Ideal

Richard Garner and Thomas Streicher, 908-913 abstract | pdf

27. Locally anisotropic toposes II

Jonathon Funk and Pieter Hofstra, 914-939 abstract | pdf

28. Cauchy completeness for DG-categories

Branko Nikolić, Ross Street and Giacomo Tendas, 940-963 abstract | pdf

29. Variation on a comprehensive theme

Ross Street, 964-978 abstract | pdf

30. Autocompact objects of Ab5 categories

Josef Dvořák and Jan Žemlička, 979-995 abstract | pdf

31. A note on Frobenius-Eilenberg-Moore objects in dagger 2-categories

Rowan Poklewski-Koziell, 996-1016 abstract | pdf

32. On Supercompactly and Compactly Generated Toposes

Morgan Rogers, 1017-1079 abstract | pdf

33. Cosheaves

Andrei V. Prasolov, 1080-1148 abstract | pdf

34. 2-dimensional bifunctor theorems and distributive laws

Peter F. Faul, Graham Manuell, José Siqueira, 1149-1175 abstract | pdf

35. On sifted colimits in the presence of pullbacks

Ruiyuan Chen, 1176-1193 abstract | pdf

36. On factorisation systems for Ord-enriched categories and categories of partial maps

Leonardo Larizza, 1194-1221 abstract | pdf

37. Compact closed categories and Γ-categories

Amit Sharma, 1222-1261 abstract | pdf

Foreword

The guest editors, 1-8 pdf

1. Maschke type theorems for Hopf monoids

Gabriella Böhm, 9-47 abstract | pdf

2. Van Kampen's theorem for locally sectionable maps

Ronald Brown, George Janelidze, and George Peschke, 48-64 abstract | pdf

3. A note on the categorical notions of normal subobject and of equivalence class

Dominique Bourn and Giuseppe Metere, 65-101 abstract | pdf

4. Span composition using fake pullbacks

Ross Street, 102-117 abstract | pdf

5. Closed dendroidal sets and unital operads

Ieke Moerdijk, 118-170 abstract | pdf

6. Three Easy Pieces: Imaginary seminar talks in honour of Bob Rosebrugh

Robert Paré, 171-200 abstract | pdf

7. Spatial realization of a Lie algebra and the Bar construction

Yves Félix and Daniel Tanré, 201-205 abstract | pdf

8. The comprehensive factorization of Burroni's T-functors

Walter Tholen and Leila Yeganeh, 206-249 abstract | pdf

9. The canonical intensive quality of a cohesive topos

F. Marmolejo and M. Menni, 250-279 abstract | pdf

10. Minimal accessible categories

Jiří Rosický, 280-287 abstract | pdf

11. Algebraic exponentiation for Lie algebras

Xabier García-Martínez and James R. A. Gray, 288-305 abstract | pdf

12. Isbell conjugacy and the reflexive completion

Tom Avery and Tom Leinster, 306-347 abstract | pdf

13. Extensions and Glueing in Double Categories

Susan Niefield, 348-367 abstract | pdf

14. (T,V)-Cat is extensive

Maria Manuel Clementino, 368-378 abstract | pdf

15. On the ternary commutator, I: Exact Mal'tsev categories

Cyrille Sandry Simeu and Tim Van der Linden, 379-422 abstract | pdf

16. Latent Fibrations: Fibrations for Categories of Partial Maps

Robin Cockett, Geoff Cruttwell, Jonathan Gallagher, and Dorette Pronk, 423-491 abstract | pdf

17. Presentations of clusters and strict free-cocompletions

Erwan Beurier, Dominique Pastor and René Guitart, 492-513 abstract | pdf

18. Intrinsic Schreier special objects

Andrea Montoli, Diana Rodelo, and Tim Van der Linden, 514-555 abstract | pdf

* The Editors of TAC wish to thank Marino Gran, Michael Johnson, Walter Tholen, and R.J. Wood who acted as guest editors for this special volume.

1. The word problem for double categories

Antonin Delpeuch, 1-18 abstract | pdf

2. Braided skew monoidal categories

John Bourke and Stephen Lack, 19-63 abstract | pdf

3. Completely distributive enriched categories are not always continuous

Hongliang Lai and Dexue Zhang, 64-88 abstract | pdf

4. The 2-Chu-Dialectica construction and the polycategory of multivariable adjunctions

Michael Shulman, 89-136 abstract | pdf

5. Small categories of homological dimension one

Karimah Sweet and Charles Ching-An Cheng, 137-154 abstract | pdf

6. Spec(Z) and the Gromov Norm

Alain Connes and Caterina Consani, 155-178 abstract | pdf

7. Morita invariance of equivariant Lusternik-Schnirelmann category and invariant topological complexity

A. Angel, H. Colman, M. Grant and J. Oprea, 179-195 abstract | pdf

8. L'-localization in an ∞-topos

Marco Vergura, 196-227 abstract | pdf

9. Rank-based persistence

Mattia G. Bergomi and Pietro Vertechi, 228-260 abstract | pdf

10. Augmented virtual double categories

Seerp Roald Koudenburg, 261-325 abstract | pdf

11. A new Galois structure in the category of internal preorders

Alberto Facchini, Carmelo Finocchiaro and Marino Gran, 326-349 abstract | pdf

12. Exact sequences in the enchilada category

M. Eryüzlü, S. Kaliszewski, and John Quigg, 350-370 abstract | pdf

13. Homotopy theory with marked additive categories

Ulrich Bunke, Alexander Engel, Daniel Kasprowski, and Christoph Winges, 371-416 abstract | pdf

14. Symmetric monoidal categories and Γ-categories

Amit Sharma, 417-512 abstract | pdf

15. Orbifolds of Reshetikhin-Turaev TQFTs

Nils Carqueville, Ingo Runkel, Gregor Schaumann, 513-561 abstract | pdf

16. Fibrations of AU-contexts beget fibrations of toposes

Sina Hazratpour and Steven Vickers, 562-593 abstract | pdf

17. Shifted double Lie-Rinehart algebras

Johan Leray, 594-621 abstract | pdf

18. Cubical model categories and quasi-categories

Brice Le Grignou, 622-664 abstract | pdf

19. Multiple vector bundles: cores, splittings and decompositions

Malte Heuer and Madeleine Jotz Lean, 665-699 abstract | pdf

20. Network Models

John C. Baez, John Foley, Joe Moeller, and Blake S. Pollard, 700-744 abstract | pdf

21. The folk model category structure on strict ω-categories is monoidal

Dimitri Ara and Maxime Lucas, 745-808 abstract | pdf

22. Cocompletion of restriction categories

Richard Garner and Daniel Lin, 809-844 abstract | pdf

23. A localization of bicategories via homotopies

Descotte M.E., Dubuc E.J., and Szyld M., 845-874 abstract | pdf

24. Weak model categories in classical and constructive mathematics

Simon Henry, 875-958 abstract | pdf

25. Lax limits of model categories

Yonatan Harpaz, 959-978 abstract | pdf

26. A recipe for black box functors

Brendan Fong and Maru Sarazola, 979-1011 abstract | pdf

27. Classification of Constructible Cosheaves

Justin Curry and Amit Patel, 1012-1047 abstract | pdf

28. Higher Segal spaces via higher excision

Tashi Walde, 1048-1086 abstract | pdf

29. Cohesive toposes of sheaves on monoids of continuous endofunctions of the unit interval

Luis Jesús Turcio, 1087-1100 abstract | pdf

30. On the construction of limits and colimits in ∞-categories

Emily Riehl and Dominic Verity, 1101-1158 abstract | pdf

31. Monoidal Grothendieck Construction

Joe Moeller and Christina Vasilakopoulou, 1159-1207 abstract | pdf

32. Exponentiability in Double Categories and the Glueing Construction

Susan Niefield, 1208-1226 abstract | pdf

33. Segal enriched categories and applications

Hugo V. Bacard, 1227-1267 abstract | pdf

34. An intrinsic approach to the non-abelian tensor product via internal crossed squares

Davide di Micco and Tim Van der Linden, 1268-1311 abstract | pdf

35. Homotopies in Grothendieck fibrations

Joseph Helfer, 1312-1378 abstract | pdf

36. Lax orthogonal factorisations in ordered structures

Maria Manuel Clementino and Ignacio López Franco, 1379-1423 abstract | pdf

37. Lax Familial Representability and Lax Generic Factorizations

Charles Walker, 1424-1475 abstract | pdf

38. Information structures and their cohomology

Juan Pablo Vigneaux, 1476-1529 abstract | pdf

39. Weighted normal commutator as the Huq commutator in points

Vaino Tuhafeni Shaumbwa, 1530-1545 abstract | pdf

40. The law of excluded middle in the simplicial model of type theory

Chris Kapulkin and Peter LeFanu Lumsdaine, 1546-1548 abstract | pdf

41. Transfer of a generalised groupoid action along a Morita equivalence

Giorgi Arabidze, 1549-1563 abstract | pdf

42. PROPs for involutive monoids and involutive bimonoids

Daniel Graves, 1564-1575 abstract | pdf

43. The Existential Completion

Davide Trotta, 1576-1607 abstract | pdf

44. Internal split opfibrations and cofunctors

Bryce Clarke, 1608-1633 abstract | pdf

45. Formal composition of hybrid systems

Jared Culbertson, Paul Gustafson, Daniel E. Koditschek, and Peter F. Stiller, 1634-1682 abstract | pdf

46. On bicolimits of C*-categories

Jamie Antoun and Christian Voigt, 1683-1725 abstract | pdf

47. Filtered cocategories

Volodymyr Lyubashenko, 1726-1770 abstract | pdf

48. Structured cospans

John C. Baez and Kenny Courser, 1771-1822 abstract | pdf

49. Metric Spaces of Extreme Points

Ernie Manes, 1823-1832 abstract | pdf

50. A Categorical Reduction System for Linear Logic

Ryu Hasegawa, 1833-1870 abstract | pdf

51. A characterisation of the category of compact Hausdorff spaces

Vincenzo Marra and Luca Reggio, 1871-1906 abstract | pdf

52. Internal partial combinatory algebras and their slices

Jetze Zoethout, 1907-1952 abstract | pdf

Table of contents also available in .pdf format.

1. Lifting PIE limits with strict projections

Martin Szyld, 1-12 abstract | pdf

2. Involutive categories, colored *-operads and quantum field theory

Marco Benini, Alexander Schenkel and Lukas Woike, 13-57 abstract | pdf

3. On the relative projective space

Matias Data and Juliana Osorio, 58-79 abstract | pdf

4. Lifting bicategories into double categories: The globularily generated condition

Juan Orendain, 80-108 abstract | pdf

5. Distributors and the comprehensive factorization system for internal groupoids

Giuseppe Metere, 109-120 abstract | pdf

6. Six operations formalism for generalized operads

Benjamin C. Ward, 121-169 abstract | pdf

7. A probability monad as the colimit of spaces of finite samples

Tobias Fritz and Paolo Perrone, 170-220 abstract | pdf

8. Cluster-tilting subcategories in extriangulated categories

Panyue Zhou and Bin Zhu, 221-242 abstract | pdf

9. Topoi of parametrized objects

Marc Hoyois, 243-248 abstract | pdf

10. Majority categories

Michael Anton Hoefnagel, 249-268 abstract | pdf

11. Categorification of pre-Lie Algebras and solutions of 2-graded classical Yang-Baxter equations

Yunhe Sheng, 269-294 abstract | pdf

12. The formal theory of multimonoidal monads

Gabriella Bohm, 295-348 abstract | pdf

13. The operadic nerve, relative nerve and the Grothendieck construction

Jonathan Beardsley and Liang Ze Wong, 349-374 abstract | pdf

14. Well-closed subschemes of noncommutative schemes

D. Rogalski, 375-404 abstract | pdf

15. Affine geometric spaces in tangent categories

R. F. Blute, G. S. H. Cruttwell, and R. B. B. Lucyshyn-Wright, 405-437 abstract | pdf

16. A note on the categorical congruence distributivity

Dominique Bourn, 438-455 abstract | pdf

17. Colimits of monoids

Hans-E. Porst, 456-467 abstract | pdf

18. Limits in dagger categories

Chris Heunen and Martti Karvonen, 468-513 abstract | pdf

19. Fibred pseudo double categories for game semantics

Clovis Eberhart, Tom Hirschowitz, 514-572 abstract | pdf

20. Quotient categories and phases

Sean Tull, 573-603 abstract | pdf

21. Left-invariant vector fields on a Lie 2-group

Eugene Lerman, 604-634 abstract | pdf

22. Strictification tensor product of 2-categories

Branko Nikolic, 635-661 abstract | pdf

23. Coequalizers and free triples, II

Michael Barr, John Kennison, and R. Raphael, 662-683 abstract | pdf

24. A universal characterisation of codescent objects

Alexander S. Corner, 684-713 abstract | pdf

25. Monic skeleta, Boundaries, Aufhebung, and the meaning of `one-dimensionality'

M. Menni, 714-735 abstract | pdf

26. The genuine operadic nerve

Peter Bonventre, 736-780 abstract | pdf

27. Homotopy theory with *-categories

Ulrich Bunke, 781-853 abstract | pdf

28. On spans with right fibred right adjoints

J. R. A. Gray, 854-882 abstract | pdf

29. Weak units, universal cells, and coherence via universality for bicategories

Amar Hadzihasanovic, 883-960 abstract | pdf

30. Biproducts and commutators for noetherian forms

Francois Koch Van Niekerk, 961-992 abstract | pdf

31. Adjunction up to automorphism

D. Tambara, 993-1035 abstract | pdf

32. Characterization of left coextensive varieties of universal algebras

David Neal Broodryk, 1036-1038 abstract | pdf

33. The tangent bundle of a model category

Yonatan Harpaz, Joost Nuiten, Matan Prasma, 1039-1072 abstract | pdf

34. Weak $\infty$-categories via terminal coalgebras

Eugenia Cheng and Tom Leinster, 1073-1133 abstract | pdf

35. On Finitary Functors

Jiri Adamek, Stefan Milius, Lurdes Sousa and Thorsten Wissmann, 1134-1164 abstract | pdf

36. A note on internal object action representability of 1-cat groups and crossed modules

Pako Ramasu, 1165-1178 abstract | pdf

37. Finitely Presentable Algebras For Finitary Monads

J. Adamek, S. Milius, L. Sousa and T. Wissmann, 1179-1195 abstract | pdf

38. The Zassenhaus lemma in star-regular categories

Olivette Ngaha Ngaha and Florence Sterck, 1196-1219 abstract | pdf

39. A model structure on prederivators for (∞,1)-categories

D. Fuentes-Keuthan, M. Kedziorek and M. Rovelli, 1220-1245 abstract | pdf

40. A unified framework for notions of algebraic theory

Soichiro Fujii, 1246-1316 abstract | pdf

41. Distributive laws between the Three Graces

Murray Bremner and Martin Markl, 1317-1342 abstract | pdf

42. Free globularly generated double categories I

Juan Orendain, 1343-1385 abstract | pdf

43. Products and coequalizers in pointed categories

Michael Hoefnagel, 1386-1400 abstract | pdf

44. The dual of compact ordered spaces is a variety

Marco Abbadini, 1401-1439 abstract | pdf

45. Models of Linear Logic based on the Schwartz $\varepsilon$-product

Yoann Dabrowski and Marie Kerjean, 1440-1525 abstract | pdf

46. Categories of weak fractions

Pierre-Alain Jacqmin, 1526-1551 abstract | pdf

Return to top.

Table of contents also available in .pdf format.

1. Spans of cospans in a topos

Daniel Cicala and Kenny Courser, 1-22 abstract | pdf

2. Actor of a crossed module of Leibniz algebras

José Manuel Casas, Rafael Fernández-Casado, Xabier García-Martínez, Emzar Khmaladze, 23-42 abstract | pdf

3. On fibrant objects in model categories

Valery Isaev, 43-66 abstract | pdf

4. Dualizing cartesian and cocartesian fibrations

Clark Barwick, Saul Glasman and Denis Nardin, 67-94 abstract | pdf

5. Contravariance through enrichment

Michael Shulman, 95-130 abstract | pdf

6. Spans of cospans

Daniel Cicala, 131-147 abstract | pdf

7. Regular patterns, substitudes, Feynman categories and operads

Michael Batanin, Joachim Kock, and Mark Weber, 148-192 abstract | pdf

8. A construction of certain weak colimits and an exactness property of the 2-category of categories

Descotte M.E., Dubuc E.J., Szyld M., 193-215 abstract | pdf

9. A Brauer-Clifford-Long group for the category of dyslectic Hopf Yetter-Drinfel'd (S,H)-module algebras

Thomas Guedenon and Allen Herman, 216-252 abstract | pdf

10. Nearly locally presentable categories

L. Positselski and J. Rosicky, 253-264 abstract | pdf

11. A characterization of final functors between internal groupoids in exact categories

Alan S. Cigoli, 265-275 abstract | pdf

12. Generating the algebraic theory of C(X): the case of partially ordered compact spaces

Dirk Hofmann, Renato Neves, and Pedro Nora, 276-295 abstract | pdf

13. On the normally ordered tensor product and duality for Tate objects

O. Braunling, M. Groechenig, A. Heleodoro, J. Wolfson, 296-349 abstract | pdf

14. Revisiting the canonicity of canonical triangulations

Moritz Groth, 350-389 abstract | pdf

15. Pseudo-Kan extensions and descent theory

Fernando Lucatelli Nunes, 390-444 abstract | pdf

16. Lax pullback complements and pullbacks of spans

Seyed Naser Hosseini, Walter Tholen, and Leila Yeganeh, 445-475 abstract | pdf

17. Double power monad preserving adjunctions are Frobenius

Christopher Townsend, 476-491 abstract | pdf

18. Regularity vs. constructive complete (co)distributivity

Hongliang Lai and Lili Shen, 492-522 abstract | pdf

19. Stability for inner fibrations revisited

Danny Stevenson, 523-536 abstract | pdf

20. Higher isotropy

J. Funk, P. Hofstra, and S. Khan, 537-582 abstract | pdf

21. Theory of interleavings on categories with a flow

V. de Silva, E. Munch, A. Stefanou, 583-607 abstract | pdf

22. Decorated corelations

Brendan Fong, 608-643 abstract | pdf

23. A parallel section functor for 2-vector bundles

Christoph Schweigert and Lukas Woike, 644-690 abstract | pdf

24. Spheres as Frobenius objects

Djordje Baralic, Zoran Petric and Sonja Telebakovic, 691-726 abstract | pdf

25. Props in network theory

John C. Baez, Brandon Coya, Franciscus Rebro, 727-783 abstract | pdf

26. Spark complexes on good effective orbifold atlases categorically

Cheng-Yong Du, Lili Shen and Xiaojuan Zhao, 784-812 abstract | pdf

27. The Ehresmann-Schein-Nambooripad Theorem for inverse categories

Darien DeWolf and Dorette Pronk, 813-831 abstract | pdf

28. On the geometric notion of connection and its expression in tangent categories

Rory B. B. Lucyshyn-Wright, 832-866 abstract | pdf

29. Crossed products of crossed modules of Hopf monoids

J.N. Alonso Alvarez, J.M. Fernandez Vilaboa, and R. Gonzalez Rodriguez, 868-897 abstract | pdf

30. Coalgebroids in monoidal bicategories and their comodules

Ramon Abud Alcala, 898-963 abstract | pdf

31. Tube representations and twisting of graded categories

J. Bhowmick, S. Ghosh, N. Rakshit, and M. Yamashita, 964-987 abstract | pdf

32. On a higher structure on operadic deformation complexes

Boris Shoikhet, 988-1030 abstract | pdf

33. New exactness conditions involving split cubes in protomodular categories

J. R. A. Gray and N. Martins-Ferreira, 1030-1058 abstract | pdf

34. $T_0$ topological spaces and $T_0$ posets in the topos of M-sets

M.M. Ebrahimi, M. Mahmoudi, and A.H. Nejah, 1059-1071 abstract | pdf

35. A tangent category alternative to the Faa di Bruno construction

Jean-Simon P. Lemay, 1072-1110 abstract | pdf

36. Polynomials, fibrations and distributive laws

Tamara von Glehn, 1111-1144 abstract | pdf

37. Linear distributivity with negation, star-autonomy, and Hopf monads

Masahito Hasegawa and Jean-Simon P. Lemay, 1145-1157 abstract | pdf

38. A compositional framework for passive linear networks

John C. Baez and Brendan Fong, 1158-1222 abstract | pdf

39. Coarse-graining open Markov processes

John C. Baez and Kenny Courser, 1223-1268 abstract | pdf

40. Category theory for genetics I:mutations and sequence alignments

Remy Tuyeras, 1269-1317 abstract | pdf

41. The localic isotropy group of a topos

Simon Henry, 1318-1345 abstract | pdf

42. On finitely aligned left cancellative small categories, Zappa-Szep products and Exel-Pardo algebras

Erik Bedos, S. Kaliszewski, John Quigg, and Jack Spielberg, 1346-1406 abstract | pdf

Return to top.

Table of contents also available in .pdf format.

1. A structure theorem for quasi-Hopf bimodule coalgebras

Daniel Bulacu, 1-30 abstract | pdf

2. Simplicial Nerve of an $A_\infty$-category

Giovanni Faonte, 31-52 abstract | pdf

3. C-systems defined by universe categories: presheaves

Vladimir Voevodsky, 53-112 abstract | pdf

4. The $(\Pi,\lambda)$-structures on the C-systems defined by universe categories

Vladimir Voevodsky, 113-121 abstract | pdf

5. Bourn-normal monomorphisms in regular Mal'tsev categories

Giuseppe Metere, 122-147 abstract | pdf

6. Homotopy theory for algebras over polynomial monads

M. A. Batanin and C. Berger, 148-253 abstract | pdf

7. A note on injective hulls of posemigroups

Changchun Xia, Shengwei Han, Bin Zhao, 254-257 abstract | pdf

8. Witt vectors and truncation posets

Vigleik Angeltveit, 258-285 abstract | pdf

9. Classifying tangent structures using Weil algebras

Poon Leung, 286-337 abstract | pdf

10. KZ-monadic categories and their logic

Jiri Adamek and Lurdes Sousa, 338-379 abstract | pdf

11. Corelations are the prop for extraspecial commutative Frobenius monoids

Brandon Coya and Brendan Fong, 380-395 abstract | pdf

12. Monoid-like definitions of cyclic operad

Jovana Obradovic, 396-436 abstract | pdf

13. Building a model category out of multiplier ideal sheaves

Seunghun Lee, 437-487 abstract | pdf

14. A categorical approach to Picard-Vessiot theory

Andreas Maurischat, 488-525 abstract | pdf

15. Epireflective subcategories and formal closure operators

Mathieu Duckerts-Antoine, Marino Gran, and Zurab Janelidze, 526-546 abstract | pdf

16. Algebraic databases

Patrick Schultz, David I. Spivak, Christina Vasilakopoulou, and Ryan Wisnesky, 547-619 abstract | pdf

17. The two out of three property in ind-categories and a convenient model category of spaces

Ilan Barnea, 620-651 abstract | pdf

18. Frobenius algebras and homotopy fixed points of group actions on bicategories

Jan Hesse, Christoph Schweigert, and Alessandro Valentino, 652-681 abstract | pdf

19. A presentation of bases for parametrized iterativity

Jiri Adamek, Stefan Milius and Jiri Velebil, 682-718 abstract | pdf

20. Closure operators in abelian categories and spectral spaces

Abhishek Banerjee, 719-735 abstract | pdf

21. Lax distributive laws for topology, II

Hongliang Lai, Lili Shen and Walter Tholen, 736-768 abstract | pdf

22. A property of effectivization and its uses in categorical logic

Vasileios Aravantinos-Sotiropoulos and Panagis Karazeris, 769-779 abstract | pdf

23. Levi categories and graphs of groups

Mark V. Lawson and Alistair R. Wallis, 780-802 abstract | pdf

24. Metric spaces and SDG

Anders Kock, 803-822 abstract | pdf

25. A unifying approach to the acyclic models method and other lifting lemmas

Leonard Guetta, 823-834 abstract | pdf

26. Connections in tangent categories

J.R.B. Cockett and G.S.H. Cruttwell, 835-888 abstract | pdf

27. Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings

Ettore Aldrovandi, 889-969 abstract | pdf

28. A Urysohn type lemma for groupoids

Madalina Roxana Buneci, 970-994 abstract | pdf

29. A bicategory of decorated cospans

Kenny Courser, 995-1027 abstract | pdf

30. The canonical 2-gerbe of a holomorphic vector bundle

Markus Upmeier, 1028-1049 abstract | pdf

31. Classifiers for monad morphisms and adjunction morphisms

Dimitri Zaganidis, 1050-1097 abstract | pdf

32. Free objects over posemigroups in the category PoSgr_v

Shengwei Han, Changchun Xia, Xiaojuan Gu, 1098-1106 abstract | pdf

33. Combinatorics of past-similarity in higher dimensional transition systems

Philippe Gaucher, 1107-1164 abstract | pdf

34. A Dold-Kan theorem for simplicial Lie algebras

P. Carrasco and A.M. Cegarra, 1165-1212 abstract | pdf

35. Localization of enriched categories and cubical sets

Tyler Lawson, 1213-1221 abstract | pdf

36. Coexponentiability and Projectivity: Rigs, Rings, and Quantales

S.B. Niefield and R.J. Wood, 1222-1228 abstract | pdf

37. Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads

Gabriella Böhm, 1229-1257 abstract | pdf

38. Fibered multiderivators and (co)homological descent

Fritz Hörmann, 1258-1362 abstract | pdf

39. Kan's combinatorial spectra and their sheaves revisited

Ruian Chen, Igor Kriz and Ales Pultr, 1363-1396 abstract | pdf

40. Operads and phylogenetic trees

John C. Baez and Nina Otter, 1396-1453 abstract | pdf

41. Topological properties of non-Archimedean approach spaces

Eva Colebunders and Karen Van Opdenbosch, 1454-1484 abstract | pdf

42. Mal'tsev objects, $R_1$-spaces and ultrametric spaces

Thomas Weighill, 1485-1500 abstract | pdf

43. Action representability via spans and prefibrations

J. R. A. Gray, 1501-1521 abstract | pdf

44. Approximate categorical structures

Abdelkrim Aliouche and Carlos Simpson, 1522-1562 abstract | pdf

45. Stability properties characterising n-permutable categories

Pierre-Alain Jacqmin, Diana Rodelo, 1563-1587 abstract | pdf

46. A characterization of the Huq commutator

Vaino Tuhafeni Shaumbwa, 1588-1600 abstract | pdf

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Table of contents also available in pdf format.

1. The Euler characteristic of an enriched category

Kazunori Noguchi and Kohei Tanaka, 1-30 abstract | pdf

2. The heart of a combinatorial model category

Zhen Lin Low, 31-62 abstract | pdf

3. On the magnitude of a finite dimensional algebra

Joseph Chuang, Alastair King and Tom Leinster, 63-72 abstract | pdf

4. A two-dimensional Birkhoff's theorem

Matej Dostal, 73-100 abstract | pdf

5. Enriched algebraic theories and monads for a system of arities

Rory B. B. Lucyshyn-Wright, 101-137 abstract | pdf

6. Relative symmetric monoidal closed categories I: Autoenrichment and change of base

Rory B. B. Lucyshyn-Wright, 138-174 abstract | pdf

7. Transfinite limits in topos theory

Moritz Kerz, 175-200 abstract | pdf

8. A characterization of central extensions in the variety of quandles

Valérian Even, Marino Gran and Andrea Montoli, 201-216 abstract | pdf

9. On biadjoint triangles

Fernando Lucatelli Nunes, 217-256 abstract | pdf

10. Some insights on bicategories of fractions: representations and compositions of 2-morphisms

Matteo Tommasini, 257-329 abstract | pdf

11. Stacks and sheaves of categories as fibrant objects, II

Alexandru E. Stanculescu, 330-364 abstract | pdf

12. Spectra of compact regular frames

Guram Bezhanishvili, David Gabelaia, Mamuka Jibladze, 365-383 abstract | pdf

13. A cotriple construction of a simplicial algebra used in the definition of higher Chow groups

Jason Polak, 384-387 abstract | pdf

14. Construction of categorical bundles from local data

Saikat Chatterjee, Amitabha Lahiri and Ambar N. Sengupta, 388-417 abstract | pdf

15. Partial linearity and partial natural Mal'tsevness

Dominique Bourn, 418-443 abstract | pdf

16. Relative internal actions

James Richard Andrew Gray and Tamar Janelidze-Gray, 444-461 abstract | pdf

17. Right delocalization of model categories

Bruce R Corrigan-Salter, 462-476 abstract | pdf

18. The morphism axiom for n-angulated categories

Emilie Arentz-Hansen, Petter Andreas Bergh and Marius Thaule, 477-483 abstract | pdf

19. The snail lemma

Enrico M. Vitale, 484-501 abstract | pdf

20. Linear structures on locales

Pedro Resende and Joao Paulo Santos, 502-541 abstract | pdf

21. Representation and character theory of finite categorical groups

Nora Ganter and Robert Usher, 542-570 abstract | pdf

22. Classical and relative realizability

Jaap van Oosten and Tingxiang Zou, 571-593 abstract | pdf

23. The linearity of traces in monoidal categories and bicategories

Kate Ponto and Michael Shulman, 594-689 abstract | pdf

24. The local Joyal model structure

Nicholas J. Meadows, 690-711 abstract | pdf

25. Homotopy locally presentable enriched categories

Stephen Lack and Jiri Rosicky, 712-754 abstract | pdf

26. Compact closed bicategories

Michael Stay, 755-798 abstract | pdf

27. Strict $\omega$-categories are monadic over polygraphs

Francois Metayer, 799-806 abstract | pdf

28. The Fermat functors

Enxin Wu, 807-832 abstract | pdf

29. Enriched Yoneda lemma

Vladimir Hinich, 833-838 abstract | pdf

30. Projectivity, continuity and adjointness: quantales, Q-posets and Q-modules

Susan Niefield, 839-851 abstract | pdf

31. Tannaka theory over sup-lattices and descent for topoi

Eduardo J. Dubuc and Martin Szyld, 852-906 abstract | pdf

32. On the representations of 2-groups in Baez-Crans 2-vector spaces

Benjamin A. Heredia and Josep Elgueta, 907-927 abstract | pdf

33. Compositories and gleaves

Cecilia Flori and Tobias Fritz, 928-988 abstract | pdf

34. On Evrard's homotopy fibrant replacement of a functor

Boris Shoikhet, 989-1015 abstract | pdf

35. Monads on dagger categories

Chris Heunen and Martti Karvonen, 1016-1043 abstract | pdf

36. Products of families of types and $(\Pi,\lambda)$-structures on C-systems

Vladimir Voevodsky, 1044-1094 abstract | pdf

37. A functorial approach to Dedekind completions and the representation of vector lattices and l-algebras by normal functions

G. Bezhanishvili, P. J. Morandi, B. Olberding, 1095-1133 abstract | pdf

38. Cosheafification

Andrei V. Prasolov, 1134-1175 abstract | pdf

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Table of contents also available in pdf format.

1. On strong homotopy for quasi-schemoids

Katsuhiko Kuribayashi, 1-14 abstract | pdf

2. Model categories with simple homotopy categories

Jean-Marie Droz and Inna Zakharevich, 15-39 abstract | pdf

3. Weak braided monoidal categories and their homotopy colimits

Mirjam Solberg, 40-48 abstract | pdf

4. Un théorème A de Quillen pour les 2-foncteurs lax

Jonathan Chiche, 49-85 abstract | pdf

5. Algebraic Kan extensions in double categories

Seerp Roald Koudenburg, 86-146 abstract | pdf

6. Bicategorical homotopy pullbacks

A.M. Cegarra, B.A. Heredia, J.Remedios, 147-205 abstract | pdf

7. Characteristic subobjects in semi-abelian categories

Alan S. Cigoli and Andrea Montoli, 206-228 abstract | pdf

8. Limit closures of classes of commutative rings

Michael Barr, John F. Kennison, R. Raphael, 229-304 abstract | pdf

9. Partial-sup lattices

Toby Kenney, 305-331 abstract | pdf

10. Lax formal theory of monads, monoidal approach to bicategorical structures and generalized operads

Dimitri Chikhladze, 332-386 abstract | pdf

11. A cocategorical obstruction to tensor products of Gray-categories

John Bourke and Nick Gurski, 387-409 abstract | pdf

12. Normalizers, centralizers and action accessibility

J. R. A. Gray, 410-432 abstract | pdf

13. Operadic definitions of weak $n$-category: coherence and comparisons

Thomas Cottrell, 433-488 abstract | pdf

14. Slicing sites and semireplete factorization systems

Thorsten Palm, 489-526 abstract | pdf

15. Notes on commutation of limits and colimits

Marie Bjerrum, Peter Johnstone, Tom Leinster, William F. Sawin, 527-532 abstract | pdf

16. Polynomials in categories with pullbacks

Mark Weber, 533-598 abstract | pdf

17. Extensive categories and the size of an orbit

Ernie Manes, 599-619 abstract | pdf

18. Cartesian differential storage categories

R. Blute, J.R.B. Cockett, and R.A.G. Seely, 620-686 abstract | pdf

19. The accessibility rank of weak equivalences

G. Raptis and J. Rosický, 687-703 abstract | pdf

20. A model structure on internal categories in simplicial sets

Geoffroy Horel, 704-750 abstract | pdf

21. Categories enriched over a quantaloid: Algebras

Qiang Pu and Dexue Zhang, 751-774 abstract | pdf

22. An algebraic definition of ($\infty$,n)-categories

Camell Kachour, 775-807 abstract | pdf

23. Reflexivity and dualizability in categorified linear algebra

Martin Brandenburg, Alexandru Chirvasitu, and Theo Johnson-Freyd, 808-835 abstract | pdf

24. Categories in control

John C. Baez and Jason Erbele, 836-881 abstract | pdf

25. Actions in modified categories of interest with application to crossed modules

Y. Boyaci, J. M. Casas, T. Datuashvili and E. O. Uslu, 882-908 abstract | pdf

26. Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness

F. W. Lawvere and M. Menni, 909-932 abstract | pdf

27. On the second cohomology categorical group and a Hochschild-Serre 2-exact sequence

A.R. Garzon and E.M. Vitale, 933-984 abstract | pdf

28. Skew-monoidal reflection and lifting theorems

Stephen Lack and Ross Street, 985-1000 abstract | pdf

29. Deligne groupoid revisited

Paul Bressler, Alexander Gorokhovsky, Ryszard Nest and Boris Tsygan, 1001-1016 abstract | pdf

30. Finite categories with pushouts

D. Tambara, 1017-1031 abstract | pdf

31. Reduced smooth stacks?

Giorgio Trentinaglia, 1032-1066 abstract | pdf

32. Cyclic homology arising from adjunctions

Niels Kowalzig, Ulrich Krähmer, and Paul Slevin, 1067-1095 abstract | pdf

33. Decorated cospans

Brendan Fong, 1096-1120 abstract | pdf

34. A note on transport of algebraic structures

Henrik Holm, 1121-1131 abstract | pdf

35. Generalized covering space theories

Jeremy Brazas, 1132-1162 abstract | pdf

36. Building a Model Category out of cofibrations and fibrations

Seunghun Lee, 1163-1180 abstract | pdf

37. A C-system defined by a universe category

Vladimir Voevodsky, 1181-1214 abstract | pdf

38. Intercategories

Marco Grandis and Robert Paré, 1215-1255 abstract | pdf

39. Stacks of Ann-Categories and their morphisms

Ettore Aldrovandi, 1256-1286 abstract | pdf

40. Segal group actions

Matan Prasma, 1287-1305 abstract | pdf

41. On reflective subcategories of locally presentable categories

J. Adamek and J. Rosicky, 1306-1318 abstract | pdf

42. Gauge invariant surface holonomy and monopoles

Arthur J. Parzygnat, 1319-1428 abstract | pdf

43. Transformation double categories associated to 2-group actions

Jeffrey C. Morton and Roger Picken, 1429-1468 abstract | pdf

44. Proximity biframes and compactifications of completely regular ordered spaces

Guram Bezhanishvili and Patrick J. Morandi, 1469-1500 abstract | pdf

45. $A_\infty$-morphisms with several entries

Volodymyr Lyubashenko, 1501-1551 abstract | pdf

46. Homotopy unital $A_\infty$-morphisms with several entries

Volodymyr Lyubashenko, 1552-1623 abstract | pdf

47. The waves of a total category

R.J. Wood, 1624-1646 abstract | pdf

48. Limits of abstract elementary classes

M. Lieberman, J. Rosicky, 1647-1658 abstract | pdf

49. Operads as polynomial 2-monads

Mark Weber, 1659-1712 abstract | pdf

50. Internal algebra classifiers as codescent objects of crossed internal categories

Mark Weber, 1713-1792 abstract | pdf

51. Algebras of open dynamical systems on the operad of wiring diagrams

Dmitry Vagner, David I. Spivak, and Eugene Lerman, 1793-1822 abstract | pdf

52. Mutation pairs and triangulated quotients

Zengqiang Lin and Minxiong Wang, 1823-1840 abstract | pdf

53. Profinite topological spaces

G. Bezhanishvili, D. Gabelaia, M. Jibladze, P. J. Morandi, 1841-1863 abstract | pdf

54. Algebraically coherent categories

Alan S. Cigoli, James R. A. Gray and Tim Van der Linden, 1864-1905 abstract | pdf

55. Groupoids in categories with pretopology

Ralf Meyer and Chenchang Zhu, 1906-1998 abstract | pdf

56. On the 3-representations of groups and the 2-categorical traces

Wei Wang, 1999-2047 abstract | pdf

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Table of contents also available in pdf format.

1. Some stability properties of epimorphism classes

Dali Zangurashvili, 1-16 abstract | pdf

2. Erratum to `Towards a homotopy theory of higher dimensional transition systems'

Philippe Gaucher, 17-20 abstract | pdf

3. On the image of the almost strict Morse n-category under almost strict n-functors

Sonja Hohloch, 21-47 abstract | pdf

4. Obvious natural morphisms of sheaves are unique

Ryan Cohen Reich, 48-99 abstract | pdf

5. Mapping Spaces of Gray-Categories

Björn Gohla, 100-187 abstract | pdf

6. Analytic spectrum of rig categories

Frederic Paugam, 188-197 abstract | pdf

7. A Galois theory for monoids

Andrea Montoli, Diana Rodelo and Tim Van der Linden, 198-214 abstract | pdf

8. Twisted actions of categorical groups

Saikat Chatterjee, Amitabha Lahiri, and Ambar N. Sengupta, 215-255 abstract | pdf

9. The theory and practice of Reedy categories

Emily Riehl and Dominic Verity, 256-301 abstract | pdf

10. Finite products in partial morphism categories

S.N. Hosseini, A.R. Shir Ali Nasab, 302-314 abstract | pdf

11. Duality in non-abelian algebra I. From cover relations to Grandis ex2-categories

Zurab Janelidze and Thomas Weighill, 315-331 abstract | pdf

12. On the infinity category of homotopy Leibniz algebras

David Khudaverdyan, Norbert Poncin, Jian Qiu, 332-370 abstract | pdf

13. Projective lines as groupoids with projection structure

Anders Kock, 371-388 abstract | pdf

14. Toward categorical risk measure theory

Takanori Adachi, 389-405 abstract | pdf

15. Topological functors as total categories

Richard Garner, 406-421 abstract | pdf

16. A Bayesian characterization of relative entropy

John C. Baez and Tobias Fritz, 422-456 abstract | pdf

17. Extending obstructions to noncommutative functorial spectra

Benno van den Berg and Chris Heunen, 457-474 abstract | pdf

18. Enriched factorization systems

Rory B. B. Lucyshyn-Wright, 475-495 abstract | pdf

19. Sequential multicategories

Claudio Pisani, 496-541 abstract | pdf

20. Continuous cohesion over sets

Matias Menni, 542-568 abstract | pdf

21. On deformations of pasting diagrams, II

Tej Shrestha and D. N. Yetter, 569-608 abstract | pdf

22. Realizable homotopy colimits

Beatriz Rodriguez Gonzalez, 609-634 abstract | pdf

23. Constructing model categories with prescribed fibrant objects

Alexandru E. Stanculescu, 635-653 abstract | pdf

24. Stacks and sheaves of categories as fibrant objects, I

Alexandru E. Stanculescu, 654-695 abstract | pdf

25. The weakly globular double category of fractions of a category

Simona Paoli, Dorette Pronk, 696-774 abstract | pdf

26. Diagrammatic characterisation of enriched absolute colimits

Richard Garner, 775-780 abstract | pdf

27. On pointwise Kan extensions in double categories

Seerp Roald Koudenburg, 781-818 abstract | pdf

28. A Serre-Swan theorem for gerbe modules on étale Lie groupoids

Christoph Schweigert, Christopher Tropp and Alessandro Valentino, 819-835 abstract | pdf

29. Bicategorical fibration structures and stacks

Dorette A. Pronk and Michael A. Warren, 836-873 abstract | pdf

30. More on geometric morphisms between realizability toposes

Eric Faber and Jaap van Oosten, 874-895 abstract | pdf

31. Completion, closure, and density relative to a monad, with examples in functional analysis and sheaf theory

Rory B. B. Lucyshyn-Wright, 896-928 abstract | pdf

32. Iterated icons

Eugenia Cheng and Nick Gurski, 929-977 abstract | pdf

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Table of contents also available in dvi or pdf format.

1. The monoidal structure of strictification

Nick Gurski, 1-23 abstract | dvi | ps | pdf

2. Free products of higher operad algebras

Mark Weber, 24-65 abstract | dvi | ps | pdf

3. Duality for distributive spaces

Dirk Hofmann, 66-122 abstract | dvi | ps | pdf

4. Semiunital semimonoidal categories (Applications to semirings and semicorings)

Jawad Abuhlail, 123-149 abstract | dvi | ps | pdf

5. On the monad of internal groupoids

Dominique Bourn, 150-165 abstract | dvi | ps | pdf

6. Tannaka duality and convolution for duoidal categories

Thomas Booker and Ross Street, 166-205 abstract | dvi | ps | pdf

7. Traced *-autonomous categories are compact closed

Tamás Hajgató and Masahito Hasegawa, 206-212 abstract | dvi | ps | pdf

8. Tightly bounded completions

Marta Bunge, 213-240 abstract | dvi | ps | pdf

9. Geometric morphisms of realizability toposes

Peter Johnstone, 241-249 abstract | dvi | ps | pdf

10. Diagonal model structures

J.F. Jardine, 250-268 abstract | dvi | ps | pdf

11. Homotopy theories of diagrams

J.F. Jardine, 269-303 abstract | dvi | ps | pdf

12. n-tuple groupoids and optimally coupled factorizations

Dany Majard, 304-331 abstract | pdf

13. Codensity and the ultrafilter monad

Tom Leinster, 332-370 abstract | dvi | ps | pdf

14. No-iteration pseudomonads

F. Marmolejo and R.J. Wood, 371-402 abstract | dvi | ps | pdf

15. Tensors, monads and actions

Gavin J. Seal, 403-434 abstract | dvi | ps | pdf

16. Bounded Archimedean l-algebras and Gelfand-Neumark-Stone duality

Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding, 435-475 abstract | dvi | ps | pdf

17. Connections on non-Abelian gerbes and their holonomy

Urs Schreiber and Konrad Waldorf, 476-540 abstract | dvi | ps | pdf

18. Subgroupoids and quotient theories

Henrik Forssell, 541-551 abstract | dvi | ps | pdf

19. Sur les types d'homotopie modélisés par les $\infty$-groupoides stricts

Dimitri Ara, 552-576 abstract | dvi | ps | pdf

20. Categories enriched over a quantaloid: Isbell adjunctions and Kan adjunctions

Lili Shen and Dexue Zhang, 577-615 abstract | dvi | ps | pdf

21. Enriched indexed categories

Michael Shulman, 616-695 abstract | dvi | ps | pdf

22. Tight spans, Isbell completions and semi-tropical modules

Simon Willerton, 696-732 abstract | pdf

23. The algebra of the nerves of omega-categories

Richard Steiner, 733-779 abstract | dvi | ps | pdf

24. Complicial structures in the nerves of omega-categories

Richard Steiner, 780-803 abstract | dvi | ps | pdf

25. Multitensor lifting and strictly unital higher category theory

Michael Batanin, Denis-Charles Cisinski and Mark Weber, 804-856 abstract | dvi | ps | pdf

26. Multitensors as monads on categories of enriched graphs

Mark Weber, 857-932 abstract | dvi | ps | pdf

27. A double categorical model of weak 2-categories

Simona Paoli and Dorette Pronk, 933-980 abstract | dvi | ps | pdf

28. Forms and exterior differentiation in Cartesian differential categories

G.S.H. Cruttwell, 981-1001 abstract | dvi | ps | pdf

29. Relative Mal'tsev categories

Tomas Everaert, Julia Goedecke, Tamar Janelidze-Gray and Tim Van der Linden, 1002-1021 abstract | dvi | ps | pdf

30. On theories of superalgebras of differentiable functions

David Carchedi and Dmitry Roytenberg, 1022-1098 abstract | dvi | ps | pdf

31. Tannaka--Krein duality for compact quantum homogeneous spaces. I. General theory

Kenny De Commer and Makoto Yamashita, 1099-1138 abstract | dvi | ps | pdf

32. The Gleason cover of a realizability topos

Peter Johnstone, 1139-1152 abstract | dvi | ps | pdf

33. Galois theories of commutative semigroups via semilattices

Isabel A. Xarez and Joao J. Xarez, 1153-1169 abstract | dvi | ps | pdf

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Table of contents also available in dvi or pdf format.

Introduction

The guest editors, 1 dvi | ps | pdf

1. Remarks on exactness notions pertaining to pushouts

Richard Garner, 2-9 abstract | dvi | ps | pdf

2. Exponentiability via double categories

Susan Niefield, 10-26 abstract | dvi | ps | pdf

3. On the axioms for adhesive and quasiadhesive categories

Richard Garner and Stephen Lack, 27-46 abstract | dvi | ps | pdf

4. The core of adjoint functors

Ross Street, 47-64 abstract | dvi | ps | pdf

5. Weakly Mal'tsev categories and strong relations

Zurab Janelidze and Nelson Martins-Ferreira, 65-79 abstract | dvi | ps | pdf

6. Symmetry of regular diamonds, the Goursat property, and subtractivity

Marino Gran, Zurab Janelidze, Diana Rodelo and Aldo Ursini, 80-96 abstract | dvi | ps | pdf

7. Exact completions and small sheaves

Michael Shulman, 97-173 abstract | dvi | ps | pdf

8. The Ursini commutator as normalized Smith-Pedicchio commutator

Sandra Mantovani, 174-188 abstract | dvi | ps | pdf

9. Higher central extensions via commutators

Diana Rodelo and Tim Van der Linden, 189-209 abstract | dvi | ps | pdf

10. Descent in monoidal categories

Bachuki Mesablishvili, 210-221 abstract | dvi | ps | pdf

11. The *-autonomous category of uniform sup semi-lattices

Michael Barr, John F. Kennison, and R. Raphael, 222-241 abstract | dvi | ps | pdf

12. Lawvere completeness as a topological property

Serdar Sozubek, 242-262 abstract | dvi | ps | pdf

13. Generalized Hopf modules for bimonads

Marcelo Aguiar and Stephen U. Chase, 263-326 abstract | dvi | ps | pdf

14. Proper maps for lax algebras and the Kuratowski-Mrówka theorem

Maria Manuel Clementino and Walter Tholen, 327-346 abstract | dvi | ps | pdf

15. On actions and strict actions in homological categories

Manfred Hartl and Bruno Loiseau, 347-392 abstract | dvi | ps | pdf

16. Composition of modules for lax functors

Robert Paré, 393-444 abstract | dvi | ps | pdf

17. Elementary quotient completion

Maria Emilia Maietti and Giuseppe Rosolini, 445-463 abstract | dvi | ps | pdf

18. An equational metalogic for monadic equational systems

Marcelo Fiore, 464-492 abstract | dvi | ps | pdf

* The Editors of TAC wish to thank Marino Gran, George Janelidze, Stephen Lack, John MacDonald and Walter Tholen who acted as guest editors for this special volume.

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Table of contents also available in dvi or pdf format.

1. Kan extensions and lax idempotent pseudomonads

F. Marmolejo and R.J. Wood, 1-29 abstract | dvi | ps | pdf

2. On the iteration of weak wreath products

Gabriella Böhm, 30-59 abstract | dvi | ps | pdf

3. On diagram-chasing in double complexes

George M. Bergman, 60-96 abstract | dvi | ps | pdf

4. Commutative monads as a theory of distributions

Anders Kock, 97-131 abstract | dvi | ps | pdf

5. Closed categories vs. closed multicategories

Oleksandr Manzyuk, 132-175 abstract | dvi | ps | pdf

6. Syntactic characterizations of properties of classifying toposes

Olivia Caramello, 176-193 abstract | dvi | ps | pdf

7. Note on star-autonomous comonads

Craig Pastro, 194-203 abstract | dvi | ps | pdf

8. A characterization of representable intervals

Michael A. Warren, 204-232 abstract | dvi | ps | pdf

9. Graphical Methods for Tannaka duality of weak bialgebras and weak Hopf algebras

Micah Blake McCurdy, 232-280 abstract | pdf

10. Notes on Bimonads and Hopf Monads

Bachuki Mesablishvili and Robert Wisbauer, 281-303 abstract | dvi | ps | pdf

11. The coalgebraic structure of cell complexes

Thomas Athorne, 304-330 abstract | dvi | ps | pdf

12. Congruences of Morita equivalent small categories

Valdis Laan, 331-337 abstract | dvi | ps | pdf

13. Injective hulls of partially ordered monoids

J. Lambek, Michael Barr, John F. Kennison, R. Raphael, 338-348 abstract | dvi | ps | pdf

14. Biequivalences in tricategories

Nick Gurski, 349-384 abstract | dvi | ps | pdf

15. Skew monoidales, skew warpings and quantum categories

Stephen Lack and Ross Street, 385-402 abstract | dvi | ps | pdf

16. A presheaf interpretation of the generalized Freyd conjecture

Anna Marie Bohmann and J. P. May, 403-411 abstract | dvi | ps | pdf

17. Range categories I: General theory

J.R.B. Cockett, Xiuzhan Guo and Pieter Hofstra, 412-452 abstract | dvi | ps | pdf

18. Range categories II: Towards regularity

J.R.B. Cockett, Xiuzhan Guo and Pieter Hofstra, 453-500 abstract | dvi | ps | pdf

19. Opetopes and chain complexes

Richard Steiner, 501-519 abstract | pdf

20. Modeling stable one-types

Niles Johnson, Angélica M. Osorno, 520-537 abstract | dvi | ps | pdf

21. Yoneda representations of flat functors and classifying toposes

Olivia Caramello, 538-553 abstract | dvi | ps | pdf

22. Bimonadicity and the explicit basis property

Matias Menni, 554-581 abstract | dvi | ps | pdf

23. Duality and traces for indexed monoidal categories

Kate Ponto and Michael Shulman, 582-659 abstract | pdf

24. Isotropy and crossed toposes

Jonathon Funk, Pieter Hofstra and Benjamin Steinberg, 660-709 abstract | dvi | ps | pdf

25. Site characterizations for geometric invariants of toposes

Olivia Caramello, 710-728 abstract | dvi | ps | pdf

26. Span, cospan, and other double categories

Susan Niefield, 729-742 abstract | dvi | ps | pdf

27. Tangled circuits

R. Rosebrugh, N. Sabadini and R. F. C. Walters, 743-767 abstract | dvi | ps | pdf

28. Décalage and Kan's simplicial loop group functor

Danny Stevenson, 768-787 abstract | dvi | ps | pdf

29. Internal categories, anafunctors and localisations

David Michael Roberts, 788-829 abstract | dvi | ps | pdf

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Table of contents also available in dvi or pdf format.

1. A category of quantum categories

Dimitri Chikhladze, 1-37 abstract | dvi | ps | pdf

2. A remark about the Connes fusion tensor product

Andreas Thom, 38-50 abstract | dvi | ps | pdf

3. Remarks on punctual local connectedness

Peter Johnstone, 51-63 abstract | dvi | ps | pdf

4. Comparative smootheology

Andrew Stacey, 64-117 abstract | dvi | ps | pdf

5. Monoidal functor categories and graphic Fourier transforms

Brian J. Day, 118-141 abstract | dvi | ps | pdf

6. Reflective-coreflective equivalence

Erik Bédos, S. Kaliszewski, and John Quigg, 142-179 abstract | dvi | ps | pdf

7. An embedding theorem for adhesive categories

Stephen Lack, 180-188 abstract | dvi | ps | pdf

8. Model-categories of coalgebras over operads

Justin R. Smith, 189-246 abstract | dvi | ps | pdf

9. A small observation on co-categories

Peter LeFanu Lumsdaine, 247-250 abstract | dvi | ps | pdf

10. Higher categorified algebras versus bounded homotopy algebras

David Khudaverdyan, Ashis Mandal, and Norbert Poncin, 250-275 abstract | dvi | ps | pdf

11. Symmetry and Cauchy completion of quantaloid-enriched categories

Hans Heymans and Isar Stubbe, 276-294 abstract | dvi | ps | pdf

12. Towards a homotopy theory of higher dimensional transition systems

Philippe Gaucher, 294-341 abstract | dvi | ps | pdf

13. Covariant presheaves and subalgebras

Ulrich Höhle, 342-367 abstract | dvi | ps | pdf

14. On involutive monoidal categories

J.M. Egger, 368-393 abstract | dvi | ps | pdf

15. The Faà di Bruno construction

J.R.B. Cockett and R.A.G. Seely, 394-425 abstract | dvi | ps | pdf

16. Semidirect products and crossed modules in varieties of right $\Omega$-loops

Edward B. Inyangala, 426-435 abstract | dvi | ps | pdf

17. Yoneda theory for double categories

Robert Paré, 436-489 abstract | dvi | ps | pdf

18. Flows: cocyclic and almost cocyclic

Michael Barr, John F. Kennison, and R. Raphael, 490-507 abstract | dvi | ps | pdf

19. Countable meets in coherent spaces with applications to the cyclic spectrum

Michael Barr, John F. Kennison, and R. Raphael, 508-532 abstract | dvi | ps | pdf

20. On reflective-coreflective equivalence and associated pairs

Erik Bédos, S. Kaliszewski, and John Quigg, 533-536 abstract | dvi | ps | pdf

21. Differential restriction categories

J.R.B. Cockett, G.S.H. Cruttwell, and J. D. Gallagher, 537-613 abstract | dvi | ps | pdf

22. Symbolic dynamics and the category of graphs

Terrence Bisson and Aristide Tsemo, 614-640 abstract | dvi | ps | pdf

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Table of contents also available in dvi or pdf format.

1. Bicategories of spans as cartesian bicategories

Stephen Lack, R.F.C. Walters, and R.J. Wood, 1-24 abstract | dvi | ps | pdf

2. The Frobenius relations meet linear distributivity

J.M. Egger, 25-38 abstract | dvi | ps | pdf

3. Joyal's arithmetic universe as list-arithmetic pretopos

Maria Emilia Maietti, 39-83 abstract | dvi | ps | pdf

4. Monads as extension systems - no iteration is necessary

F. Marmolejo and R. J. Wood, 84-113 abstract | dvi | ps | pdf

5. On a conjecture by J.H.Smith

George Raptis, 114-116 abstract | dvi | ps | pdf

6. Topos theoretic aspects of semigroup actions

Jonathon Funk and Pieter Hofstra, 117-147 abstract | dvi | ps | pdf

7. Transversal homotopy theory

Jonathan Woolf, 148-178 abstract | pdf

8. On modified Reedy and modified projective model structures

Mark W. Johnson, 179-208 abstract | dvi | ps | pdf

9. Finitely presentable morphisms in exact sequences

Michel Hébert, 209-220 abstract | dvi | ps | pdf

10. The Hopf algebra of Möbius intervals

F. W. Lawvere and M. Menni, 221-265 abstract | dvi | ps | pdf

11. Tensor products of sup-lattices and generalized sup-arrows

T. Kenney and R.J. Wood, 266-287 abstract | dvi | ps | pdf

12. Lax presheaves and exponentiability

Susan Niefield, 288-301 abstract | dvi | ps | pdf

13. The span construction

Robert Dawson, Robert Paré, Dorette Pronk, 302-377 abstract | dvi | ps | pdf

14. On *-autonomous categories of topological modules

Michael Barr, John F. Kennison, and R. Raphael, 378-393 abstract | dvi | ps | pdf

15. A logic for categories

Claudio Pisani, 394-417 abstract | dvi | ps | pdf

16. On the duality between trees and disks

David Oury, 418-450 abstract | dvi | ps | pdf

17. Internal profunctors and commutator theory; applications to extensions classification and categorical Galois Theory

Dominique Bourn, 451-488 abstract | dvi | ps | pdf

18. Higher Dimensional Algebra VII: Groupoidification

John C. Baez, Alexander E. Hoffnung, and Christopher D. Walker, 489-553 abstract | dvi | ps | pdf

19. Hopf monoidal comonads

Dimitri Chikhladze, Stephen Lack, and Ross Street, 554-563 abstract | dvi | ps | pdf

20. Strictification of categories weakly enriched in symmetric monoidal categories

Bertrand J. Guillou, 564-579 abstract | dvi | ps | pdf

21. A unified framework for generalized multicategories

G.S.H. Cruttwell and Michael A. Shulman, 580-655 abstract | dvi | ps | pdf

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Table of contents also available in dvi or pdf format.

Foreword

The guest editors, 1-6 dvi | ps | pdf

1. Action accessibility for categories of interest

Andrea Montoli, 7-21 abstract | dvi | ps | pdf

2. Homology of n-fold groupoids

Tomas Everaert and Marino Gran, 22-41 abstract dvi | ps | pdf

3. The comprehensive factorization and torsors

Ross Street and Dominic Verity, 42-75 abstract | dvi | ps | pdf

4. Snake Lemma in incomplete relative homological categories

Tamar Janelidze, 76-91 abstract | dvi | ps | pdf

5. Monadic approach to Galois descent and cohomology

Francis Borceux, Stefaan Caenepeel and George Janelidze, 92-112 abstract | dvi | ps | pdf

6. Internal crossed modules and Peiffer Condition

Sandra Mantovani, Giuseppe Metere, 113-135 abstract | dvi | ps | pdf

7. Strongly separable morphisms in general categories

G. Janelidze and W. Tholen, 136-149 abstract | dvi | ps | pdf

8. The third cohomology group classifies double central extensions

Diana Rodelo and Tim Van der Linden, 150-169 abstract | dvi | ps | pdf

9. Star-multiplicative graphs in pointed protomodular categories

N. Martins-Ferreira, 170-198 abstract | dvi | ps | pdf

10. A metric tangential calculus

Elisabeth Burroni and Jacques Penon, 199-220 abstract | dvi | ps | pdf

11. The pointed subobject functor, 3 x 3 lemmas, and subtractivity of spans

Zurab Janelidze, 221-242 abstract | dvi | ps | pdf

12. A categorical approach to integration

Reinhard Börger, 243-250 abstract | dvi | ps | pdf

13. What are sifted colimits?

J. Adamek, J. Rosicky, E. M. Vitale, 251-260 abstract | dvi | ps | pdf

* The Editors of TAC wish to thank Andree Ehresmann, George Janelidze, Jiri Rosicky, Walter Tholen and Enrico Vitale who acted as guest editors for this special volume.

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1. Duality for CCD lattices

Francisco Marmolejo, Robert Rosebrugh, and R.J. Wood, 1-23 abstract | dvi | ps | pdf

2. On deformations of pasting diagrams

D. N. Yetter, 24-53 abstract | dvi | ps | pdf

3. Searching for more absolute CR-epic spaces

Michael Barr, John F. Kennison, and R. Raphael, 54-76 abstract | dvi | ps | pdf

4. On endomorphism algebras of separable monoidal functors

Brian Day and Craig Pastro, 77-96 abstract | dvi | ps | pdf

5. Categories with slicing

Thorsten Palm, 97-135 abstract | dvi | ps | pdf

6. Tensor-triangulated categories and dualities

Baptiste Calmès and Jens Hornbostel, 136-198 abstract | dvi | ps | pdf

7. Lois distributives. Applications aux automates stochastiques

Elisabeth Burroni, 198-221 abstract | dvi | ps | pdf

8. Algebraic colimit calculations in homotopy theory using fibred and cofibred categories

Ronald Brown and Rafael Sivera, 222-251 abstract | dvi | ps | pdf

9. Covering space theory for directed topology

Eric Goubault, Emmanuel Haucourt, Sanjeevi Krishnan, 252-268 abstract | pdf

10. On the categorical semantics of elementary linear logic

Olivier Laurent, 269-301 abstract | dvi | ps | pdf

11. Enriched orthogonality and equivalences

M. Golasinski and L. Stramaccia, 302-312 abstract | dvi | ps | pdf

12. Weak distributive laws

Ross Street, 313-320 abstract | dvi | ps | pdf

13. An embedding theorem for Hilbert categories

Chris Heunen, 321-344 abstract | dvi | ps | pdf

14. Eventually cyclic spectra of parameterized flows

John F. Kennison, 345-375 abstract | dvi | ps | pdf

15. T-catégories représentables

Jacques Penon, 376-387 abstract | dvi | ps | pdf

16. Epimorphic covers make $R^+_G$ a site, for profinite $G$

Daniel G. Davis, 388-400 abstract | dvi | ps | pdf

17. Isbell duality for modules

Michael Barr, John F. Kennison, and R. Raphael, 401-419 abstract | dvi | ps | pdf

18. Higher-dimensional categories with finite derivation type

Yves Guiraud and Philippe Malbos, 420-478 abstract | pdf

19. A brief review of abelian categorifications

Mikhail Khovanov, Volodymyr Mazorchuk and Catharina Stroppel, 479-508 abstract | ps | pdf

20. Algebraic categories whose projectives are explicitly free

Matías Menni, 509-541 abstract | dvi | ps | pdf

21. Vector fields and flows on differentiable stacks

Richard Hepworth, 542-587 abstract | dvi | ps | pdf

22. Homotopical interpretation of globular complex by multipointed d-space

Philippe Gaucher, 588-621 abstract | dvi | ps | pdf

23. Cartesian differential categories

R.F. Blute, J.R.B. Cockett and R.A.G. Seely, 622-672 abstract | dvi | ps | pdf

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Table of contents also available in .dvi or .ps or .pdf format.

Foreword

The guest editors, 1-6 dvi | ps | pdf

1. A convenient category for directed homotopy

L. Fajstrup and J. Rosicky, 7-20 abstract | dvi | ps | pdf

2. Limit preserving full embeddings

V. Trnkova and J. Sichler, 21-36 abstract | dvi | ps | pdf

3. Protolocalisations of exact Mal'cev categories

Francis Borceux, Marino Gran, Sandra Mantovani, 37-60 abstract | dvi | ps | pdf

4. Doubles for monoidal categories

Craig Pastro and Ross Street, 61-75 abstract | dvi | ps | pdf

5. Completions in biaffine sets

Elisabetta Felaco and Eraldo Giuli, 76-90 abstract | dvi | ps | pdf

6. Weakly Mal'cev categories

N. Martins-Ferreira, 91-117 abstract | dvi | ps | pdf

7. Extensions in the theory of lax algebras

Christoph Schubert and Gavin J. Seal, 118-151 abstract | dvi | ps | pdf

8. Approximate Mal'tsev operations

Dominique Bourn and Zurab Janelidze, 152-171 abstract | dvi | ps | pdf

9. Notes on effective descent and projectivity in quasivarieties of universal algebras

Ana Helena Roque, 172-181 abstract | dvi | ps | pdf

10. Descent for compact 0-dimensional spaces

George Janelidze and Manuela Sobral, 182-190 abstract | dvi | ps | pdf

11. Analytic functors and weak pullbacks

J. Adamek and J. Velebil, 191-209 abstract | dvi | ps | pdf

12. Relative injectivity as cocompleteness for a class of distributors

Maria Manuel Clementino and Dirk Hofmann, 210-230 abstract | dvi | ps | pdf

* The Editors of TAC wish to thank Maria Manuel Clementino, George Janelidze, Jiri Rosicky and Robert Rosebrugh who acted as guest editors for this special volume.

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Editorial Notice: Max Kelly, 5 June 1930 - 26 January 2007

Ross Street, 1-4 pdf

1. Locally cartesian closed categories without chosen constructions

Erik Palmgren, 5-17 abstract | dvi | ps | pdf

2. Generalized Brown representability in homotopy categories: Erratum

Jiri Rosicky, 18-24 abstract | dvi | ps | pdf

3. Frobenius objects in cartesian bicategories

R.F.C Walters and R.J. Wood, 25-47 abstract | dvi | ps | pdf

4. Abelian groupoids and non-pointed additive categories

Dominique Bourn, 48-73 abstract | dvi | ps | pdf

5. Coherence for pseudodistributive laws revisited

F. Marmolejo and R. J. Wood, 74-84 abstract | dvi | ps | pdf

6. Balanced category theory

Claudio Pisani, 85-115 abstract | dvi | ps | pdf

7. Category-theoretic models of linear Abadi and Plotkin logic

Lars Birkedal and Rasmus E. Mogelberg and Rasmus L. Petersen, 116-151 abstract | dvi | ps | pdf

8. Kan extensions in double categories (On weak double categories, Part III)

Marco Grandis and Robert Paré, 152-185 abstract | dvi | ps | pdf

9. Fundamental pushout toposes

Marta Bunge, 186-214 abstract | dvi | ps | pdf

10. Algebraic real analysis

Peter Freyd, 215-306 abstract | dvi | ps | pdf

11. Star-autonomous functor categories

Jeff Egger, 307-333 abstract | dvi | ps | pdf

12. Colimits of representable algebra-valued functors

George M. Bergman, 334-404 abstract | dvi | ps | pdf

13. Quotients of unital $A_\infty$-categories

Volodymyr Lyubashenko and Oleksandr Manzyuk, 405-496 abstract | dvi | ps | pdf

14. Core varieties, extensivity, and rig geometry

F. William Lawvere, 497-503 abstract | dvi | ps | pdf

15. Isbell duality

Michael Barr, John F. Kennison, and R. Raphael, 504-542 abstract | dvi | ps | pdf

16. Cohomology theory in 2-categories

Hiroyuki Nakaoka, 542-604 abstract | dvi | ps | pdf

17. Propriétés universelles et extensions de Kan dérivées

Denis-Charles Cisinski, 605-649 abstract | dvi | ps | pdf

18. Framed bicategories and monoidal fibrations

Michael Shulman, 650-738 abstract | dvi | ps | pdf

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Proceedings of the International Category Theory Conference, CT 2006

The organizers, 1-3 pdf

1. Exponentiability in homotopy slices of Top and pseudo-slices of Cat

Susan Niefield, 4-18 abstract | dvi | ps | pdf

2. Components, complements and the reflection formula

Claudio Pisani, 19-40 abstract | dvi | ps | pdf

3. Axiomatic cohesion

F. William Lawvere, 41-49 abstract | dvi | ps | pdf

4. Q-modules are Q-suplattices

Isar Stubbe, 50-60 abstract | dvi | ps | pdf

5. Iterative algebras: How iterative are they?

J. Adamek, R. Borger, S. Milius, and J. Velebil, 61-92 abstract | dvi | ps | pdf

6. Cartesian bicategories II

A. Carboni, G.M. Kelly, R.F.C. Walters, and R.J. Wood, 93-124 abstract | dvi | ps | pdf

Table of contents also available in .dvi or .ps or .pdf format.

1. Bicat is not triequivalent to Gray

Stephen Lack, 1-3 abstract | dvi | ps | pdf

2. Polarized category theory, modules, and game semantics

J.R.B. Cockett and R.A.G. Seely, 4-101 abstract | dvi | ps | pdf

3. Functional analysis on normed spaces: the Banach space comparison

M. Sioen and S. Verwulgen, 102-117 abstract | dvi | ps | pdf

4. On Yetter's invariant and an extension of the Dijkgraaf-Witten invariant to categorical groups

Joao Faria Martins and Timothy Porter, 118-150 abstract | dvi | ps | pdf

5. Pullback and finite coproduct preserving functors between categories of permutation representations: Corrigendum and addendum

Elango Panchadcharam and Ross Street, 151-156 abstract | dvi | ps | pdf

6. CCD lattices in presheaf categories

G. S. H. Cruttwell, F. Marmolejo and R.J. Wood, 157-171 abstract | dvi | ps | pdf

7. Monad compositions I: general constructions and recursive distributive laws

Ernie Manes and Philip Mulry, 172-208 abstract | dvi | ps | pdf

8. Quasi locally connected toposes

Marta Bunge and Jonathon Funk, 209-239 abstract | dvi | ps | pdf

9. More morphisms between bundle gerbes

Konrad Waldorf, 240-273 abstract | dvi | ps | pdf

10. Towards an n-category of cobordisms

Eugenia Cheng and Nick Gurski, 274-302 abstract | dvi | ps | pdf

11. The theory of core algebras: its completeness

Peter Freyd, 303-320 abstract | dvi | ps | pdf

12. Higher cospans and weak cubical categories (Cospans in algebraic topology, I)

Marco Grandis, 321-347 abstract | dvi | ps | pdf

13. Coherent unit actions on regular operads and Hopf algebras

Kurusch Ebrahimi-Fard and Li Guo, 348-371 abstract | dvi | ps | pdf

14. Dense morphisms of monads

Panagis Karazeris and Jiri Velebil, 372-399 abstract | dvi | ps | pdf

15. Enriched model categories and an application to additive endomorphism spectra

Daniel Dugger and Brooke Shipley, 400-439 abstract | dvi | ps | pdf

16. Nuclei of categories with tensor products

Alexei Davydov, 440-472 abstract | dvi | ps | pdf

17. Exploring the gap between linear and classical logic

Francois Lamarche, 473-535 abstract | dvi | ps | pdf

18. On the axiomatisation of Boolean categories with and without medial

Lutz Strassburger, 536-601 abstract | dvi | ps | pdf

19. Collared cospans, cohomotopy and TQFT (cospans in algebraic topology, II)

Marco Grandis, 602-630 abstract | dvi | ps | pdf

20. A universal property of the monoidal 2-category of cospans of ordinals and surjections

M. Menni, N. Sabadini and R. F. C. Walters, 631-653 abstract | dvi | ps | pdf

21. Quotients of tannakian categories

J.S. Milne, 654-664 abstract | dvi | ps | pdf

22. Familial 2-functors and parametric right adjoints

Mark Weber, 665-732 abstract | dvi | ps | pdf

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Preface

The guest editors, 1-9 dvi | ps | pdf

1. The Chu construction: history of an idea

Michael Barr, 10-16 abstract | dvi | ps | pdf

2. Coherence of the double involution on *-autonomous categories

J.R.B. Cockett, M. Hasegawa and R.A.G. Seely, 17-29 abstract | dvi | ps | pdf

3. A Parigot-style linear $\lambda$-calculus for full intuitionistic linear

Valeria de Paiva and Eike Ritter, 30-48 abstract | dvi | ps | pdf

4. The Dialectica interpretation of first-order classical affine logic

Masaru Shirahata,49-79 abstract | dvi | ps | pdf

5. Approximable concepts, Chu spaces, and information systems

Guo-Qiang Zhang and Gongqin Shen, 79-102 abstract | dvi | ps | pdf

6. An extended view of the Chu-construction

Jurgen Koslowski, 103-126 abstract | dvi | ps | pdf

7. Dialectica and Chu constructions: cousins?

Valeria de Paiva, 127-152 abstract | dvi | ps | pdf

* The Editors of TAC wish to thank Valeria de Paiva and Vaughan Pratt who acted as guest editors for this special volume.

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1. Monads of effective descent type and comonadicity

Bachuki Mesablishvili, 1-45 abstract | dvi | ps | pdf

2. Action groupoid in protomodular categories

Dominique Bourn, 46-58 abstract | dvi | ps | pdf

3. Inverting weak dihomotopy equivalence using homotopy continuous flow

Philippe Gaucher, 59-83 abstract | dvi | ps | pdf

4. Frobenius algebras and ambidextrous adjunctions

Aaron D. Lauda, 84-122 abstract | dvi | ps | pdf

5. Every Grothendieck topos has a one-way site

Colin McLarty, 123-126 abstract | dvi | ps | pdf

6. Points of affine categories and additivity

A. Carboni and G. Janelidze, 127-131 abstract | dvi | ps | pdf

7. Preserving homology

Michael Barr, 132-143 abstract | dvi | ps | pdf

8. Thin fillers in the cubical nerves of omega-categories

Richard Steiner, 144-173 abstract | dvi | ps | pdf

9. Free A_\infty-categories

Volodymyr Lyubashenko and Oleksandr Manzyuk, 174-205 abstract | dvi | ps | pdf

10. A characterization of quantic quantifiers in orthomodular lattices

Leopoldo Román, 206-217 abstract | dvi | ps | pdf

11. Exponentiability in lax slices of Top

Susan Niefield, 218-235 abstract | dvi | ps | pdf

12. Closedness properties of internal relations I: A unified approach to Mal'tsev, unital and subtractive categories

Zurab Janelidze, 236-261 abstract | dvi | ps | pdf

13. Closedness properties of internal relations II: Bourn localization

Zurab Janelidze, 262-282 abstract | dvi | ps | pdf

14. Categorical structures enriched in a quantaloid: tensored and cotensored categories

Isar Stubbe, 283-306 abstract | dvi | ps | pdf

15. Stable meet semilattice fibrations and free restriction categories

J.R.B. Cockett and Xiuzhan Guo, 307-341 abstract | dvi | ps | pdf

16. TFT Construction of RCFT correlators V: Proof of modular invariance and factorisation

Jens Fjelstad, Jurgen Fuchs, Ingo Runkel and Christoph Schweigert, 342-433 abstract | ps | pdf

17. Spectra of finitely generated Boolean flows

John F. Kennison, 434-459 abstract | dvi | ps | pdf

18. Paths in double categories

R. J. MacG. Dawson, R. Paré, and D. A. Pronk, 460-521 abstract | dvi | ps | pdf

19. Numerology in topoi

Peter Freyd, 522-528 abstract | dvi | ps | pdf

20. Categorical representations of categorical groups

John W. Barrett and Marco Mackaay, 529-557 abstract | dvi | ps | pdf

21. Compactifications, C(X) and ring epimorphisms

W.D. Burgess and R. Raphael, 558-584 abstract | dvi | ps | pdf

22. On categorical crossed modules

P. Carrasco, A.R. Garzon and E.M. Vitale, 585-618 abstract | dvi | ps | pdf

23. Equivalence of 2D-multitopic category and ana-bicategory

Param Jyothi Reddy R, 619-667 abstract | ps | pdf

24. Descent for monads

Pieter Hofstra and Federico De Marchi, 668-699 abstract | dvi | ps | pdf

25. Topological *-autonomous categories

Michael Barr, 700-708 abstract | dvi | ps | pdf

26. Quotient models of a category up to directed homotopy

Marco Grandis, 709-735 abstract | dvi | ps | pdf

27. Categories of components and loop-free categories

Emmanuel Haucourt, 736-770 abstract | pdf

28. Pullback and finite coproduct preserving functors between categories of permutation representations

Elango Panchadcharam and Ross Street, 771-784 abstract | dvi | ps | pdf

29. Categorified algebra and quantum mechanics

Jeffrey Morton, 785-854 abstract | ps | pdf

30. A cohomological description of connections and curvature over posets

John E. Roberts and Giuseppe Ruzzi, 855-895 abstract | dvi | ps | pdf

31. Generating families in a topos

Toby Kenney, 896-922 abstract | dvi | ps | pdf

32. Copower objects and their applications to finiteness in topoi

Toby Kenney, 923-956 abstract | dvi | ps | pdf

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1. Predicative algebraic set theory

Steve Awodey and Michael A. Warren, 1-39 abstract | dvi | ps | pdf

2. Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads

Marcelo Fiore and Matias Menni, 40-65 abstract | dvi | ps | pdf

3. Model structures for homotopy of internal categories

T. Everaert, R.W. Kieboom and T. Van der Linden, 66-94 abstract | dvi | ps | pdf

4. The shape of a category up to directed homotopy

Marco Grandis, 95-146 abstract | dvi | ps | pdf

5. Algebraic models of intuitionistic theories of sets and classes

S. Awodey and H. Forssell, 147-163 abstract | dvi | ps | pdf

6. Generic commutative separable algebras and cospans of graphs

R. Rosebrugh, N. Sabadini and R.F.C. Walters, 164-177 abstract | dvi | ps | pdf

7. A Galois theory with stable units for simplicial sets

Joao J. Xarez, 178-193 abstract | dvi | ps | pdf

* The Editors of TAC wish to thank George Janelidze, John MacDonald, Ross Street and Walter Tholen who acted as guest editors for this special volume.

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1. Categorical structures enriched in a quantaloid: categories, distributors and functors

Isar Stubbe, 1-45 abstract | dvi | ps | pdf

2. On essential ring embeddings and the epimorphic hull of C(X)

R. Raphael, R.G. Woods, 46-52 abstract | dvi | ps | pdf

3. Absolute homology

Michael Barr, 53-59 abstract | dvi | ps | pdf

4. Thin elements and commutative shells in cubical omega-categories

Philip J. Higgins, 60-74 abstract | dvi | ps | pdf

5. Adjunction models for call-by-push-value with stacks

Paul Blain Levy, 75-110 abstract | dvi | ps | pdf

6. Abstract physical traces

Samson Abramsky and Bob Coecke, 111-124 abstract | ps | pdf

7. A monadic approach to polycategories

Juergen Koslowski, 125-156 abstract | dvi | ps | pdf

8. Introduction to coalgebra

Jiri Adamek, 157-199 abstract | dvi | ps | pdf

9. A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem

R. Brown, K.H. Kamps, and T. Porter, 200-220 abstract | dvi | ps | pdf

10. Canonical and op-canonical lax algebras

Gavin J. Seal, 221-243 abstract | dvi | ps | pdf

11. On the representability of actions in a semi-abelian category

F. Borceux, G. Janelidze and G.M. Kelly, 244-286 abstract | dvi | ps | pdf

12. Groupoid enriched categories and natural systems

Teimuraz Pirashvili, 287-293 abstract | dvi | ps | pdf

13. Every group is representable by all natural transformations of some set-functor

Libor Barto and Petr Zima, 294-309 abstract | dvi | ps | pdf

14. Classification of concrete geometrical categories

Yves Diers, 310-327 abstract | dvi | ps | pdf

15. Localic completion of generalized metric spaces I

Steven Vickers, 328-356 abstract | dvi | ps | pdf

16. Enlargements of categories

Lars Brünjes, Christian Serpé, 357-398 abstract | dvi | ps | pdf

17. Notes on enriched categories with colimits of some class

G.M. Kelly and V. Schmitt, 399-423 abstract | dvi | ps | pdf

18. Birkhoff's variety theorem with and without free algebras

Jiri Adamek and Vera Trnkova, 424-450 abstract | dvi | ps | pdf

19. Generalized Brown representability in homotopy categories

Jiri Rosicky, 451-479 abstract | dvi | ps | pdf

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Table of contents also available in .dvi or .ps or .pdf format.

Foreword

The guest editors, 1-4 dvi | ps | pdf

1. On von Neumann varieties

F. Borceux and J. Rosicky, 5-26 abstract | dvi | ps | pdf

2. Commutator theory in strongly protomodular categories

Dominique Bourn, 27-40 abstract | dvi | ps | pdf

3. On extensions of lax monads

Maria Manuel Clementino and Dirk Hofmann abstract | dvi | ps | pdf

4. Universal properties of Span

R.J.MacG. Dawson, R. Pare and D.A. Pronk, 61-85 abstract | dvi | ps | pdf

5. Derivations of categorical groups

A.R. Garzon, H. Inassaridze and A. del Rio, 86-105 abstract | dvi | ps | pdf

6. Semi-abelian monadic categories

Marino Gran and Jiri Rosicky, 106-113 abstract | dvi | ps | pdf

7. Normed combinatorial homology and noncommutative tori

Marco Grandis, 114-128 abstract | dvi | ps | pdf

8. Coalgebras, braidings, and distributive laws

Stefano Kasangian, Stephen Lack, and Enrico M. Vitale, 129-146 abstract | dvi | ps | pdf

9. Composing PROPs

Stephen Lack, 147-163 abstract | dvi | ps | pdf

10. Functorial concepts of complexity for finite automata

F. William Lawvere, 164-168 abstract | dvi | ps | pdf

11. Every small Sl-enriched category is Morita equivalent to an Sl-monoid

Bachuki Mesablishvili, 169-171 abstract | dvi | ps | pdf

12. Split structures

Robert Rosebrugh and R.J. Wood, 172-183 abstract | dvi | ps | pdf

13. The monoidal centre as a limit

Ross Street, 184-190 abstract | dvi | ps | pdf

14. Generic morphisms, parametric representations and weakly cartesian monads

Mark Weber, 191-234 abstract | dvi | ps | pdf

15. Internal monotone-light factorization for categories via preorders

Joao Xarez, 235-251 abstract | dvi | ps | pdf

* The Editors of TAC wish to thank G. Janelidze, S. Lack, F.W. Lawvere, E.M. Vitale and R.J. Wood who acted as guest editors for this special volume.

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Table of contents also available in .dvi or .ps or .pdf format.

1. Baer invariants in semi-abelian categories I: General theory

T. Everaert and T. Van der Linden, 1-33 abstract | dvi | ps | pdf

2. Simplicial approximation

J.F. Jardine, 34-72 abstract | dvi | ps | pdf

3. Operads in higher-dimensional category theory

Tom Leinster, 73-194 abstract | dvi | ps | pdf

4. Baer invariants in semi-abelian categories II: Homology

T. Everaert and T. Van der Linden, 195-224 abstract | dvi | ps | pdf

5. Notions of flatness relative to a Grothendieck topology

Panagis Karazeris, 225-236 abstract | dvi | ps | pdf

6. Moore categories

Diana Rodelo, 237-247 abstract | dvi | ps | pdf

7. Change of base for relational variable sets

Susan Niefield, 248-261 abstract | dvi | ps | pdf

8. On subgroups of the Lambek pregroup

Michael Barr, 262-269 abstract | dvi | ps | pdf

9. Algebraically closed and existentially closed substructures in categorical context

Michel Hebert, 269-298 abstract | dvi | ps | pdf

10. Vertically iterated classical enrichment

Stefan Forcey, 299-325 abstract | dvi | ps | pdf

11. Several constructions for factorization systems

Dali Zangurashvili, 326-354 abstract | dvi | ps | pdf

12. K-purity and orthogonality

Michel Hebert, 355-371 abstract | dvi | ps | pdf

13. The double powerlocale and exponentiation: A case study in geometric logic

Steven Vickers, 372-422 abstract | dvi | ps | pdf

14. Higher-dimensional algebra V: 2-Groups

John C. Baez and Aaron D. Lauda, 423-491 abstract | dvi | ps | pdf

15. Higher-dimensional algebra VI: Lie 2-algebras

John C. Baez and Alissa S. Crans, 492-538 abstract | dvi | ps | pdf

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Table of contents also available in .dvi or .ps or .pdf format.

1. Categorical models and quasigroup homotopies

George Voutsadakis, 1-14 abstract | dvi | ps | pdf

2. Morphisms and modules for poly-bicategories

J.R.B. Cockett, J. Koslowski, and R.A.G. Seely, 15-74 abstract | dvi | ps | pdf

3. The branching nerve of HDA and the Kan condition

Philippe Gaucher, 75-106 abstract | dvi | ps | pdf

4. Isomorphisms between left and right adjoints

H. Fausk, P. Hu, and J.P. May, 107-131 abstract | dvi | ps | pdf

5. The Wirthmuller isomorphism revisited

J.P. May, 132-142 abstract | dvi | ps | pdf

6. Characterization of protomodular varieties of universal algebras

Dominique Bourn and George Janelidze, 143-147 abstract | dvi | ps | pdf

7. Resolutions by polygraphs

François Métayer, 148-184 abstract | dvi | ps | pdf

8. Cubical sets and their site

Marco Grandis and Luca Mauri, 185-211 abstract | dvi | ps | pdf

9. Characterization of pointed varieties of universal algebras with normal projections

Zurab Janelidze, 212-214 abstract | dvi | ps | pdf

10. Some algebraic applications of graded categorical group theory

A.M. Cegarra and A.R. Garzon, 215-251 abstract | dvi | ps | pdf

11. Continuous categories revisited

J. Adamek, F. W. Lawvere, J. Rosicky, 252-282 abstract | dvi | ps | pdf

12. Ring epimorphisms and C(X)

Michael Barr, W.D. Burgess and R. Raphael, 283-308 abstract | dvi | ps | pdf

13. Partial toposes

Jean Bénabou and Thomas Streicher, 309-320 abstract | dvi | ps | pdf

14. Some calculus with extensive quantities: wave equation

Anders Kock and Gonzalo E. Reyes, 321-336 abstract | dvi | ps | pdf

15. Exponentiability in categories of lax algebras

Maria Manuel Clementino, Dirk Hofmann and Walter Tholen, 337-352 abstract | dvi | ps | pdf

16. The category of opetopes and the category of opetopic sets

Eugenia Cheng, 353-374 abstract | dvi | ps | pdf

17. Modules

J.R.B. Cockett, J. Koslowski, R.A.G. Seely, and R.J. Wood, 375-396 abstract | dvi | ps | pdf

18. Symmetric monoidal completions and the exponential principle among labeled combinatorial structures

Matias Menni, 397-419 abstract | dvi | ps | pdf

19. Composition-representative subsets

Gary Griffing, 420-437 abstract | dvi | ps | pdf

20. The strong amalgamation property and (effective) codescent morphisms

Dali Zangurashvili, 438-449 abstract | dvi | ps | pdf