We give a classification of substructures (= closed subbifunctors) of a given skeletally small extriangulated category by using the category of defects, in a similar way to the author’s classification of exact structures of a given additive category. More precisely, for an extriangulated category, possible substructures are in bijection with Serre subcategories of an abelian category consisting of defects of conflations. As a byproduct, we prove that for a given skeletally small additive category, the poset of exact structures on it is isomorphic to the poset of Serre subcategories of some abelian category.

中文翻译：

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通过Serre子类别对广泛分类的子结构进行分类

通过使用缺陷类别，我们对给定的骨骼较小的细化类别进行了子结构分类（=封闭的子函数），类似于作者对给定加性类别的精确结构进行分类的方法。更准确地说，对于一个被挖掘的类别，可能的子结构与阿贝尔类别的Serre子类别是双射的，后者由合并的缺陷组成。作为副产品，我们证明对于给定的骨骼较小的加性类别，其上确切结构的波状体与某些阿贝尔类别的Serre子类别的波状体同构。