Almost split triangles in pre-extriangulated categories

Colloquium Mathematicum(2022)

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摘要
We consider the notion of pre-extriangulated categories. We give some characterizations of almost split s-triangles in a pre-extriangulated category and provide necessary and sufficient conditions for the existence of such triangles. If E is an extension-closed subcategory of a pre-extriangulated category C having almost split s-triangles, we obtain necessary and sufficient conditions for E to have almost split s-triangles using the approximation properties of a certain class of objects.
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关键词
pre-extriangulated categories,almost split s-triangles,extension-closed subcategories,approximations
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