2023/11/10 by Rasool Hafezi, Hafezi, Rasool, Javad Asadollahi +3
Mathematics · #16E30 #18E05 #18E99 #18G15 #18G25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2311.05879
openalex publication_date 2023/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Higher homological algebra, basically done in the framework of an n-cluster tilting subcategory M of an abelian category A, has been the topic of several recent researches. In this paper, we study a relative version, in the sense of Auslander-Solberg, of the higher homological algebra. To this end, we consider an additive sub-bifunctor F of ExtnM( -,-) as the basis of our relative theory. This, in turn, specifies a collection of n-exact sequences in M, which allows us to delve into the relative higher homological algebra. Our results include a proof of the relative n-Auslander-Reiten duality formula, as well as an exploration of relative Grothendieck groups, among other results. As an application, we provide necessary and sufficient conditions for M to be of finite type.