Classifying Substructures of Extriangulated Categories via Serre Subcategories
Classifying Substructures of Extriangulated Categories via Serre Subcategories
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DOI：
10.1007/s10485-021-09642-0
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发表时间：
2020-05
影响因子：
0.6
通讯作者：
H. Enomoto
中科院分区：
文献类型：
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作者：
H. Enomoto
我们利用缺陷的范畴，以类似于作者对给定加性范畴的精确结构的分类的方式，给出了给定骨架小外三角范畴的子结构（=闭合子双分子）的分类。更确切地说，对于外三角化范畴，可能的子结构与由合并缺陷组成的阿贝尔范畴的六个子范畴是双射的。作为副产物，我们证明了对于给定的骨架小的可加范畴，其上的精确结构的偏序与某些阿贝尔范畴的Serre子范畴的偏序是同构的。
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.