Extension-closed subcategories in extriangulated categories

AIMS Mathematics(2022)

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摘要
In this paper, we mainly focus on extension-closed subcategories of extriangulated categories. Let X be an extension-closed subcategory. We show that if C is X-projective and there is a minimal right almost split deflation in X ending by C, then there is an s-triangle ending by C which is very similar to an Auslander-Reiten triangle in X. We also show that if the extriangulated category admits a negative first extension E-1, and X is self-orthogonal with respect to E-1, then X has an exact structure.
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关键词
extriangulated categories, extension-closed subcategories, almost split morphism, negative first extension, exact categories
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