2012/03/19 by Shiping Liu, Liu, Shiping, Puiman Ng +3
Computer Science · Mathematics · #16G20 #16G70 #18E10 #18E40 #Advanced Algebra and Logic #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1203.5009
openalex publication_date 2012/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence in A induces an almost split sequence in an exact subcategory C of A. In case A has almost split sequences and C is Hom-finite Krull-Schmidt, this provides a necessary and sufficient condition for C to have almost split sequences. Finally, we show two applications of these results.