单元的Eilenberg-Moore范畴的微分扭转理论

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-02-14 DOI:10.1016/j.jpaa.2025.107910

Divya Ahuja, Surjeet Kour

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引用次数: 0

摘要

设C是格罗滕迪克范畴，U是C上精确且保留极限的单子。在本文中，我们证明了单轴U上模的Eilenberg-Moore范畴上的每一个遗传扭转理论都是微分的。更进一步，如果δ:U δ U表示单列U上的导数，那么我们证明了U模M上的每个δ导数唯一地扩展到M的商模上的δ导数。

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Differential torsion theories on Eilenberg-Moore categories of monads

Let

C

be a Grothendieck category and U be a monad on

C

that is exact and preserves colimits. In this article, we prove that every hereditary torsion theory on the Eilenberg-Moore category of modules over a monad U is differential. Furthermore, if

δ : U ⟶ U

denotes a derivation on a monad U, then we show that every δ-derivation on a U-module M extends uniquely to a δ-derivation on the module of quotients of M.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.