Naturality of the $\infty$-Categorical Enriched Yoneda Embedding
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909244753707008 |
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| author | Ben-Moshe, Shay |
| author_facet | Ben-Moshe, Shay |
| contents | We make Hinich's $\infty$-categorical enriched Yoneda embedding natural. To do so, we exhibit it as the unit of a partial adjunction between the functor taking enriched presheaves and Heine's functor taking a tensored category to an enriched category. Furthermore, we study a finiteness condition of objects in a tensored category called being atomic, and show that the partial adjunction restricts to a (non-partial) adjunction between taking enriched presheaves and taking atomic objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00601 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Naturality of the $\infty$-Categorical Enriched Yoneda Embedding Ben-Moshe, Shay Category Theory Algebraic Topology We make Hinich's $\infty$-categorical enriched Yoneda embedding natural. To do so, we exhibit it as the unit of a partial adjunction between the functor taking enriched presheaves and Heine's functor taking a tensored category to an enriched category. Furthermore, we study a finiteness condition of objects in a tensored category called being atomic, and show that the partial adjunction restricts to a (non-partial) adjunction between taking enriched presheaves and taking atomic objects. |
| title | Naturality of the $\infty$-Categorical Enriched Yoneda Embedding |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2301.00601 |