December 2022 RELATIVE DERIVED CATEGORIES, RELATIVE SINGULARITY CATEGORIES AND RELATIVE DEFECT CATEGORIES
Hanyang You, Guodong Zhou
Rocky Mountain J. Math. 52(6): 2189-2209 (December 2022). DOI: 10.1216/rmj.2022.52.2189

Abstract

We introduce the relative Gorenstein defect category of an abelian category with respect to an admissible subcategory, generalizing the Gorenstein defect categories of P. A. Bergh, D. Jorgensen and S. Oppermann. Under a mild condition of the precovering property for the relative Gorenstein category, we show that the relative Gorenstein defect category is triangle equivalent to the relative singularity category with respect to the relative Gorenstein category.

We also introduce relative Ding projective defect categories and, under a similar condition, relate it to the relative singularity category with respect to the relative Ding projective category. Analogous results for relative Ding injective defect categories are also presented.

Citation

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Hanyang You. Guodong Zhou. "RELATIVE DERIVED CATEGORIES, RELATIVE SINGULARITY CATEGORIES AND RELATIVE DEFECT CATEGORIES." Rocky Mountain J. Math. 52 (6) 2189 - 2209, December 2022. https://doi.org/10.1216/rmj.2022.52.2189

Information

Received: 16 March 2021; Revised: 3 December 2021; Accepted: 27 January 2022; Published: December 2022
First available in Project Euclid: 28 December 2022

MathSciNet: MR4527018
zbMATH: 1516.18009
Digital Object Identifier: 10.1216/rmj.2022.52.2189

Subjects:
Primary: 16G50 , 18G25 , 18G80

Keywords: relative derived category , relative Ding defect category , relative Ding injective category , relative Ding projective category , relative Gorenstein category , relative Gorenstein defect category , relative singularity category

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

Vol.52 • No. 6 • December 2022
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