Special precovered categories of Gorenstein categories

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（8）
• 页码范围: 1553-1566
• 页数: 14页
• 语种: 英文

摘要

Let A be an abelian category and p(A) be the subcategory of A consisting of projective objects.Let l be a full,additive and self-orthogonal subcategory of A with p(A) a generator,and let g(l) be the Gorenstein subcategory of A.Then the right 1-orthogonal category g(l)⊥1 of g(l) is both projectively resolving and injectively coresolving in A.We also get that the subcategory SPC(g(l)) of A consisting of objects admitting special g(l)-precovers is closed under extensions and l-stable direct summands (*).Furthermore,if l is a generator for g(l)⊥1,then we have that SPC(g(l)) is the minimal subcategory of A containing g(l)⊥1 ∪ g(l) with respect to the property (*),and that SPC(g(l)) is l-resolving in A with a l-proper generator l.