June 22, 2024Open Access

R-Mod-enriched categories are left R-module objects of Cat (Ab) and Cat (Ab) -enriched functors

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Abstract

We establish the feasibility of investigating the theory of R-Mod-enriched categories, for any commutative and unitary ring R, through the framework of Ab-enriched category theory. In particular, we prove that the category of R-Mod-enriched categories, Cat (R-Mod), the category of R-modules inside Cat (Ab), LModₑ (Cat (Ab) ), and the category of Cat (Ab) -enriched functors, Fun^Cat (Ab) (R, Cat (Ab) ) are equivalent.

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Matteo Doni (Sat,) studied this question.

synapsesocial.com/papers/68e63c0bb6db6435875cd9e5 https://doi.org/https://doi.org/10.48550/arxiv.2406.15887

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