Weak vertical composition II: totalities
Category Theory
2023-08-22 v1
Abstract
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.
Cite
@article{arxiv.2308.09806,
title = {Weak vertical composition II: totalities},
author = {Eugenia Cheng and Alexander S. Corner},
journal= {arXiv preprint arXiv:2308.09806},
year = {2023}
}