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- W3188759154 abstract "The notion of extriangulated category was introduced by Nakaoka and Palu giving a simultaneous generalization of exact categories and triangulated categories. Our first aim is to provide an extension to extriangulated categories of Auslander's formula: for some extriangulated category $mathcal{C}$, there exists a localization sequence $operatorname{def}mathcal{C} to modmathcal{C} to operatorname{lex}mathcal{C}$, where $operatorname{lex}mathcal{C}$ denotes the full subcategory of finitely presented left exact functors and $operatorname{def}mathcal{C}$ the full subcategory of Auslander's defects. Moreover we provide a connection between the above localization sequence and the Gabriel–Quillen embedding theorem. As an application, we show that the general heart construction of a cotorsion pair $(mathcal{U}, mathcal{V})$ in a triangulated category, which was provided by Abe and Nakaoka, is the same as the construction of a localization sequence $operatorname{def}mathcal{U} to modmathcal{U} to operatorname{lex}mathcal{U}$." @default.
- W3188759154 created "2021-08-16" @default.
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- W3188759154 date "2021-10-22" @default.
- W3188759154 modified "2023-10-17" @default.
- W3188759154 title "Auslander's defects over extriangulated categories: An application for the general heart construction" @default.
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- W3188759154 doi "https://doi.org/10.2969/jmsj/84578457" @default.
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