We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloid Q. In analogy with V-category theory we discuss such things as adjoint functors, (pointwise) left Kan extensions, weighted (co)limits, presheaves and free (co)completion, Cauchy completion and Morita equivalence. With an appendix on the universality of the quantaloid Dist(Q) of Q-enriched categories and distributors.
Keywords: Quantales and quantaloids, enriched categories
2000 MSC: 06F07, 18B35, 18D20
Theory and Applications of Categories,
Vol. 14, 2005,
No. 1, pp 1-45.
http://www.tac.mta.ca/tac/volumes/14/1/14-01.dvi
http://www.tac.mta.ca/tac/volumes/14/1/14-01.ps
http://www.tac.mta.ca/tac/volumes/14/1/14-01.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/1/14-01.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/1/14-01.ps