More on soundness in the enriched context
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912665990856704 |
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| author | Tendas, Giacomo |
| author_facet | Tendas, Giacomo |
| contents | Working within enriched category theory, we further develop the use of soundness, introduced by Adámek, Borceux, Lack, and Rosický for ordinary categories. In particular we investigate: (1) the theory of locally $Φ$-presentable $\mathcal V$-categories for a sound class $Φ$, (2) the problem of whether every $Φ$-accessible $\mathcal V$-category is $Ψ$-accessible, for given sound classes $Φ\subseteqΨ$, and (3) a notion of $Φ$-ary equational theory whose $\mathcal V$-categories of models characterize algebras for $Φ$-ary monads on $\mathcal V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | More on soundness in the enriched context Tendas, Giacomo Category Theory 18D20, 18C35, 18C05, 18C15 Working within enriched category theory, we further develop the use of soundness, introduced by Adámek, Borceux, Lack, and Rosický for ordinary categories. In particular we investigate: (1) the theory of locally $Φ$-presentable $\mathcal V$-categories for a sound class $Φ$, (2) the problem of whether every $Φ$-accessible $\mathcal V$-category is $Ψ$-accessible, for given sound classes $Φ\subseteqΨ$, and (3) a notion of $Φ$-ary equational theory whose $\mathcal V$-categories of models characterize algebras for $Φ$-ary monads on $\mathcal V$. |
| title | More on soundness in the enriched context |
| topic | Category Theory 18D20, 18C35, 18C05, 18C15 |
| url | https://arxiv.org/abs/2409.00389 |