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Weakly globular double categories and weak units

Banff International Research Station for Mathematical Innovation and Discovery

Weakly globular double categories are a model of weak 2-categories based on the notion of weak globularity, and they are known to be suitably equivalent to Tamsamani 2-categories. Fair 2-categories, introduced by J. Kock, model weak 2-categories with strictly associative compositions and weak unit laws. In this talk I will illustrate how to establish a direct comparison between weakly globular double categories and fair 2-categories and prove they are equivalent after localisation with respect to the 2-equivalences. This comparison sheds new light on weakly globular double categories as encoding a strictly associative, though not strictly unital, composition, as well as the category of weak units via the weak globularity condition. Reference: S. Paoli, Weakly globular double categories and weak units, arXiv:2008.11180v1

Mathematics; Category Theory; Homological Algebra; Algebraic Topology; Algebraic Structures

video/mp4

Author affiliation: Leicester University

2023-10-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86392

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/