Let A be an abelian category and P(A)be the subcategory of A consisting of projective objects.Let C be a full,additive and self-orthogonal subcategory of A with P(A)a generator,and let G(C)be the Gorenstein subcategor...Let A be an abelian category and P(A)be the subcategory of A consisting of projective objects.Let C be a full,additive and self-orthogonal subcategory of A with P(A)a generator,and let G(C)be the Gorenstein subcategory of A.Then the right 1-orthogonal category G(C)^⊥1 of G(C)is both projectively resolving and injectively coresolving in A.We also get that the subcategory SPC(G(C))of A consisting of objects admitting special G(C)-precovers is closed under extensions and C-stable direct summands(*).Furthermore,if C is a generator for G(C)^⊥1,then we have that SPC(G(C))is the minimal subcategory of A containing G(C)^⊥1∪G(C)with respect to the property(*),and that SPC(G(C))is C-resolving in A with a C-proper generator C.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11571164)Priority Academic Program Development of Jiangsu Higher Education Institutions+1 种基金the University Postgraduate Research and Innovation Project of Jiangsu Province 2016 (Grant No. KYZZ16 0034)Nanjing University Innovation and Creative Program for PhD Candidate (Grant No. 2016011)
文摘Let A be an abelian category and P(A)be the subcategory of A consisting of projective objects.Let C be a full,additive and self-orthogonal subcategory of A with P(A)a generator,and let G(C)be the Gorenstein subcategory of A.Then the right 1-orthogonal category G(C)^⊥1 of G(C)is both projectively resolving and injectively coresolving in A.We also get that the subcategory SPC(G(C))of A consisting of objects admitting special G(C)-precovers is closed under extensions and C-stable direct summands(*).Furthermore,if C is a generator for G(C)^⊥1,then we have that SPC(G(C))is the minimal subcategory of A containing G(C)^⊥1∪G(C)with respect to the property(*),and that SPC(G(C))is C-resolving in A with a C-proper generator C.
