2025/10/08 by Yutong Zhou, Zhou, Yutong
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2510.06626
openalex publication_date 2025/10/08 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28
The notion of n-exangulated categories was introduced by Herschend-Liu-Nakaoka, which is a simultaneous generalization of n-exact categories in the sense of Jasso and (n+2)-angulated categories in the sense of Geiss-Kelier-Oppermann. Let (\mathscrC,𝔼,\mathfraks) be an n-exangulated category with enough projectives P and M a full subcategory of \mathscrC containing P. In the present paper, It is proved that a certian quotient category of \mathfraks-def(M) is abelian. We denoted by S(\mathscrC) the category of n-exangles, whose object are given by distinguished n-exangles in \mathscrC. If M=\mathscrC, we obtain that a certain ideal quotient category S(\mathscrC)/R2 is equivalent to the category of finitely presented modules mod-(\mathscrC/[P]). Furthermore, we present the quotient category S(\mathscrC)/R2 always has an abelian structure when taking n as an even number. The abelian quotient S(\mathscrC)/R2 admits some nice properties. We describe the projective objects in S(\mathscrC)/R2 and characterize the simple objects in S(\mathscrC)/R2 as Auslander-Reiten n-exangle sequences in \mathscrC.