Weakly globular double categories and weak units

Simona Paoli

doi:10.48550/arXiv.2008.11180

Weakly globular double categories and weak units

Simona Paoli^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

Research output: Working paper › Preprint

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Abstract

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.

Original language	English
Publisher	ArXiv
Number of pages	58
DOIs	https://doi.org/10.48550/arXiv.2008.11180
Publication status	Published - 10 Mar 2024

Bibliographical note

Substantially changed version, based on new definition 4.2 of the fat delta. Former section 5, now called section6, has been completely re-written with new results and proofs. Former section 8, now section 9, also partially re-written with results framed in a more general context. The main result has been moved to the new section 10

Version History

[v1] Tue, 25 Aug 2020 17:29:58 UTC (34 KB)
[v2] Sat, 15 May 2021 14:11:38 UTC (36 KB)
[v3] Thu, 1 Sep 2022 14:59:42 UTC (44 KB)
[v4] Sun, 10 Mar 2024 10:32:28 UTC (44 KB)
[v5] Fri, 14 Mar 2025 13:19:42 UTC (45 KB)

Funding

Acknowledgements This paper is partially based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the ’Higher Categories and Categorification’ program in Spring 2020. I thank the organizers for their invitation to this program. I also thank the referee for many helpful comments.

Funders	Funder number
National Science Foundation	DMS-1440140

Keywords

math.CT
math.AT
18D05, 18G30

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10.48550/arXiv.2008.11180Licence: Unspecified

2008.11180v4Submitted manuscript, 617 KBLicence: Unspecified

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Weakly globular double categories and weak units

Abstract

Bibliographical note

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Keywords

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