Enriched Locally Generated Categories
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866917013701525504 |
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| author | Di Liberti, Ivan Rosický, Jiří |
| author_facet | Di Liberti, Ivan Rosický, Jiří |
| contents | We introduce the notion of $\mathcal{M}$-locally generated category for a factorization system $(\mathcal{E},\mathcal{M})$ and study its properties. We offer a Gabriel-Ulmer duality for these categories, introducing the notion of nest. We develop this theory also from an enriched point of view. We apply this technology to Banach spaces showing that it is equivalent to the category of models of the nest of finite-dimensional Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_10980 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Enriched Locally Generated Categories Di Liberti, Ivan Rosický, Jiří Category Theory We introduce the notion of $\mathcal{M}$-locally generated category for a factorization system $(\mathcal{E},\mathcal{M})$ and study its properties. We offer a Gabriel-Ulmer duality for these categories, introducing the notion of nest. We develop this theory also from an enriched point of view. We apply this technology to Banach spaces showing that it is equivalent to the category of models of the nest of finite-dimensional Banach spaces. |
| title | Enriched Locally Generated Categories |
| topic | Category Theory |
| url | https://arxiv.org/abs/2009.10980 |