November 2023 Galois covering of pure-semisimple categories
Elham Mahdavi, Shokrollah Salarian, Razieh Vahed
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Kyoto J. Math. 63(4): 829-849 (November 2023). DOI: 10.1215/21562261-2023-0007

Abstract

Let C be a locally bounded k-category, where k is a field. We prove that C is pure-semisimple, that is, every object of Mod-C is pure-projective if and only if every family of morphisms between indecomposable finitely generated C-modules is Noetherian. Our formalism establishes the pure-semisimplicity of Galois coverings, that is, if C is a G-category with a free G-action on ind-C, then C is pure-semisimple if and only if CG is so.

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Elham Mahdavi. Shokrollah Salarian. Razieh Vahed. "Galois covering of pure-semisimple categories." Kyoto J. Math. 63 (4) 829 - 849, November 2023. https://doi.org/10.1215/21562261-2023-0007

Information

Received: 11 November 2020; Revised: 28 November 2021; Accepted: 20 January 2022; Published: November 2023
First available in Project Euclid: 18 September 2023

MathSciNet: MR4643006
Digital Object Identifier: 10.1215/21562261-2023-0007

Subjects:
Primary: 18A25
Secondary: 16D70 , 18A32

Keywords: covering functors , G-categories , orbit categories , pure-semisimple categories

Rights: Copyright © 2023 by Kyoto University

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Vol.63 • No. 4 • November 2023
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