2017/12/01 by Tiwei Zhao, Zhao, Tiwei, Zhaoyong Huang +1
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1712.00314
openalex publication_date 2017/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathscrA be an abelian category and \mathscrP(\mathscrA) the subcategory of \mathscrA consisting of projective objects. Let \mathscrC be a full, additive and self-orthogonal subcategory of \mathscrA with \mathscrP(\mathscrA) a generator, and let G(\mathscrC) be the Gorenstein subcategory of \mathscrA. Then the right 1-orthogonal category G(\mathscrC)\bot1 of G(\mathscrC) is both projectively resolving and injectively coresolving in \mathscrA. We also get that the subcategory \spc(G(\mathscrC)) of \mathscrA consisting of objects admitting special G(\mathscrC)-precovers is closed under extensions and \mathscrC-stable direct summands (*). Furthermore, if \mathscrC is a generator for G(\mathscrC)⊥1, then we have that \spc(G(\mathscrC)) is the minimal subcategory of \mathscrA containing G(\mathscrC)⊥1∪ G(\mathscrC) with respect to the property (*), and that \spc(G(\mathscrC)) is \mathscrC-resolving in \mathscrA with a \mathscrC-proper generator \mathscrC.