Tensor Enriched Categorical Generalization of the Eilenberg-Watts Theorem

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-10-10 DOI:10.1007/s10485-025-09818-y

Jaehyeok Lee

引用次数: 0

Abstract

Let b, \(b'\) be commutative monoids in a Bénabou 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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Eilenberg-Watts定理的富张量范畴推广

设b， \(b'\)是一个b矩阵中的可交换半群。从代数几何中的六函子形式出发，证明了\(b\otimes b'\)上的可交换单模的范畴等价于b， \(b'\)上右模的单模富范畴之间的共连续松弛单模富函子的范畴。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.