Weakly globular double categories and weak units
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866915196526657536 |
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| author | Paoli, Simona |
| author_facet | Paoli, Simona |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_11180 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Weakly globular double categories and weak units Paoli, Simona Category Theory Algebraic Topology 18D05, 18G30 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. |
| title | Weakly globular double categories and weak units |
| topic | Category Theory Algebraic Topology 18D05, 18G30 |
| url | https://arxiv.org/abs/2008.11180 |