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Tensor enriched categorical generalization of the Eilenberg-Watts theorem (2302.11001v6)
Published 21 Feb 2023 in math.CT, math.AC, and math.RA
Abstract: Let $b$, $b\text{ }!'$ 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 $b\otimes b\text{ }!'$ is equivalent to the category of cocontinuous lax monoidal enriched functors between the monoidal enriched categories of right modules over $b$, $b\text{ }!'$.
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