On $2$-categorical $\infty$-cosmoi
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912583840169984 |
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| author | Bourke, John Lack, Stephen |
| author_facet | Bourke, John Lack, Stephen |
| contents | Recently Riehl and Verity have introduced $\infty$-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those $\infty$-cosmoi which are in fact $2$-categories; we shall refer to these as $2$-cosmoi. We show that each $2$-category with flexible limits gives rise to a $2$-cosmos whose distinguished class of isofibrations consists of the normal isofibrations. Many examples arise in this way, and we show that such $2$-cosmoi are minimal as Cauchy-complete $2$-cosmoi. Finally, we investigate accessible $2$-cosmoi and develop a few aspects of their basic theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16002 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $2$-categorical $\infty$-cosmoi Bourke, John Lack, Stephen Category Theory 18N60, 18C35, 18D20, 18N40 Recently Riehl and Verity have introduced $\infty$-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those $\infty$-cosmoi which are in fact $2$-categories; we shall refer to these as $2$-cosmoi. We show that each $2$-category with flexible limits gives rise to a $2$-cosmos whose distinguished class of isofibrations consists of the normal isofibrations. Many examples arise in this way, and we show that such $2$-cosmoi are minimal as Cauchy-complete $2$-cosmoi. Finally, we investigate accessible $2$-cosmoi and develop a few aspects of their basic theory. |
| title | On $2$-categorical $\infty$-cosmoi |
| topic | Category Theory 18N60, 18C35, 18D20, 18N40 |
| url | https://arxiv.org/abs/2305.16002 |