Notions of enriched purity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917875770458112 |
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| author | Rosický, Jiří Tendas, Giacomo |
| author_facet | Rosický, Jiří Tendas, Giacomo |
| contents | We introduce enriched notions of purity depending on the left class $\mathcal E$ of a factorization system on the base $\mathcal V$ of enrichment. Ordinary purity is given by the class of surjective mappings in the category of sets. Under specific assumptions, covering enrichment over quantale-valued metric spaces, $ω$-complete posets, and quasivarieties, we characterize the $(λ,\mathcal E)$-injectivity classes of locally presentable $\mathcal V$-categories in terms of closure under a class of limits, $λ$-filtered colimits, and $(λ,\mathcal E)$-pure subobjects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11957 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Notions of enriched purity Rosický, Jiří Tendas, Giacomo Category Theory 18D20, 18A32, 18F75, 18G35 We introduce enriched notions of purity depending on the left class $\mathcal E$ of a factorization system on the base $\mathcal V$ of enrichment. Ordinary purity is given by the class of surjective mappings in the category of sets. Under specific assumptions, covering enrichment over quantale-valued metric spaces, $ω$-complete posets, and quasivarieties, we characterize the $(λ,\mathcal E)$-injectivity classes of locally presentable $\mathcal V$-categories in terms of closure under a class of limits, $λ$-filtered colimits, and $(λ,\mathcal E)$-pure subobjects. |
| title | Notions of enriched purity |
| topic | Category Theory 18D20, 18A32, 18F75, 18G35 |
| url | https://arxiv.org/abs/2303.11957 |