Tensor Enriched Categorical Generalization of the Eilenberg-Watts Theorem
Category Theory
2025-10-20 v8 Commutative Algebra
Rings and Algebras
Abstract
Let , 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 is equivalent to the category of cocontinuous lax monoidal enriched functors between the monoidal enriched categories of right modules over , .
Cite
@article{arxiv.2302.11001,
title = {Tensor Enriched Categorical Generalization of the Eilenberg-Watts Theorem},
author = {Jaehyeok Lee},
journal= {arXiv preprint arXiv:2302.11001},
year = {2025}
}
Comments
The paper was accepted at 16th June 2025, and published at 10th October 2025 in the journal `Applied Categorical Structures'. Some minor typos were corrected during publication process. This is the final version of the paper, and the content is identical to that of the published paper