On effective descent $\mathcal V$-functors and familial descent morphisms
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914638631796736 |
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| author | Prezado, Rui |
| author_facet | Prezado, Rui |
| contents | We study effective descent $ \mathcal V $-functors for cartesian monoidal categories $ \mathcal V $ with finite limits. This study is carried out via the properties enjoyed by the $2$-functor $ \mathcal V \mapsto \mathsf{Fam}(\mathcal V) $, results about effective descent of bilimits of categories, and the fact that the enrichment $2$-functor preserves certain bilimits. Since these results rely on an understanding of (effective) descent morphisms in $ \mathsf{Fam}(\mathcal V) $, we briefly study those epimorphisms when $ \mathcal V $ is a regular category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04042 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On effective descent $\mathcal V$-functors and familial descent morphisms Prezado, Rui Category Theory 18N10, 18F20, 18D20, 18B50, 18A25, 18A35 We study effective descent $ \mathcal V $-functors for cartesian monoidal categories $ \mathcal V $ with finite limits. This study is carried out via the properties enjoyed by the $2$-functor $ \mathcal V \mapsto \mathsf{Fam}(\mathcal V) $, results about effective descent of bilimits of categories, and the fact that the enrichment $2$-functor preserves certain bilimits. Since these results rely on an understanding of (effective) descent morphisms in $ \mathsf{Fam}(\mathcal V) $, we briefly study those epimorphisms when $ \mathcal V $ is a regular category. |
| title | On effective descent $\mathcal V$-functors and familial descent morphisms |
| topic | Category Theory 18N10, 18F20, 18D20, 18B50, 18A25, 18A35 |
| url | https://arxiv.org/abs/2305.04042 |