2018/12/11 by Lars Winther Christensen, Christensen, Lars Winther, Sergio Estrada +3
Mathematics · Physics and Astronomy · #18G35 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Primary 16E05. Secondary 18G25 #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1812.04402
openalex publication_date 2018/12/11 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
We introduce a notion of total acyclicity associated to a subcategory of an\nabelian category and consider the Gorenstein objects they define. These\nGorenstein objects form a Frobenius category, whose induced stable category is\nequivalent to the homotopy category of totally acyclic complexes. Applied to\nthe flat-cotorsion theory over a coherent ring, this provides a new description\nof the category of cotorsion Gorenstein flat modules; one that puts it on equal\nfooting with the category of Gorenstein projective modules.\n