论文标题
Schur的精确类别的引理意味着Abelian
Schur's lemma for exact categories implies abelian
论文作者
论文摘要
我们表明，对于给定的确切类别，在半纤维（成对的hom-ordorthonal砖集）和长度宽子类别（精确延伸延伸长度覆盖长度的Abelian子类别）之间存在双歧射击。特别是，当且仅当简单的对象形成半iBrick时，即Schur的引理时，我们才表明一个长度确切的类别是Abelian。
We show that for a given exact category, there exists a bijection between semibricks (pairwise Hom-orthogonal set of bricks) and length wide subcategories (exact extension-closed length abelian subcategories). In particular, we show that a length exact category is abelian if and only if simple objects form a semibrick, that is, the Schur's lemma holds.
