Univalent Enriched Categories and the Enriched Rezk Completion
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914622264573952 |
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| author | van der Weide, Niels |
| author_facet | van der Weide, Niels |
| contents | Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this paper, we study univalent enriched categories. We prove that all essentially surjective and fully faithful functors between univalent enriched categories are equivalences, and we show that every enriched category admits a Rezk completion. Finally, we use the Rezk completion for enriched categories to construct univalent enriched Kleisli categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Univalent Enriched Categories and the Enriched Rezk Completion van der Weide, Niels Logic in Computer Science Category Theory Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this paper, we study univalent enriched categories. We prove that all essentially surjective and fully faithful functors between univalent enriched categories are equivalences, and we show that every enriched category admits a Rezk completion. Finally, we use the Rezk completion for enriched categories to construct univalent enriched Kleisli categories. |
| title | Univalent Enriched Categories and the Enriched Rezk Completion |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2401.11752 |