Tensor Enriched Categorical Generalization of the Eilenberg-Watts Theorem

Jaehyeok Lee

doi:10.1007/s10485-025-09818-y

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arXiv · 2302.11001

Tensor Enriched Categorical Generalization of the Eilenberg-Watts Theorem

Jaehyeok Lee

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Abstract

Let $b$, $b'$ be commutative monoids in a B\'{e}nabou cosmos. Motivated by six-functor formalisms in algebraic geometry, we prove that the category of commutative monoids over $b\otimes b'$ is equivalent to the category of cocontinuous lax monoidal enriched functors between the monoidal enriched categories of right modules over $b$, $b'$.

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BibTeX RIS

Jaehyeok Lee. 2023-02-21. Tensor Enriched Categorical Generalization of the Eilenberg-Watts Theorem. https://doi.org/10.1007/s10485-025-09818-y

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