Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2406.15887 |
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Sommario:
- We establish the feasibility of investigating the theory of $R\text{-}\mathrm{Mod}$-enriched categories, for any commutative and unitary ring $R$, through the framework of $\mathbb{A}\mathrm{b}$-enriched category theory. In particular, we prove that the category of $R$-$\mathrm{Mod}$-enriched categories, $Cat(R$-$\mathrm{Mod})$, the category of $\underline{R}$-modules inside $Cat(\mathbb{A}\mathrm{b})$, $\mathrm{LMod}_{\underline{R}}(Cat(\mathbb{A}\mathrm{b}))$, and the category of $Cat(\mathbb{A}\mathrm{b})$-enriched functors, $Fun^{Cat(\mathbb{A}\mathrm{b})}(\underline{\underline{R}},Cat(\mathbb{A}\mathrm{b}))$ are equivalent.