Weak vertical composition II: totalities

Eugenia Cheng and Alexander S. Corner

We continue our study of semi-strict tricategories in which the only weakness is in vertical composition. We assemble the doubly-degenerate such tricategories into a 2-category, defining weak functors and transformations. We exhibit a biadjoint biequivalence between this 2-category and the 2-category of braided (weakly) monoidal categories, braided (weakly) monoidal functors, and monoidal transformations.

Keywords: tricategory, degenerate, braided monoidal category, enrichment, icon

2020 MSC: 18D05, 18D10, 18D20

Theory and Applications of Categories, Vol. 41, 2024, No. 31, pp 995-1043.

Published 2024-08-21.

http://www.tac.mta.ca/tac/volumes/41/31/41-31.pdf

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