Weakly globular double categories and weak units

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...

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Bibliographic Details
Published inarXiv.org
Main Author Paoli, Simona
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.03.2024
Subjects
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Composition
Equivalence
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Summary: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 paper we 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.
ISSN:2331-8422