2017/09/20 by Herschend, Martin, Liu, Yu, Nakaoka, Hiroyuki
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1709.06689
For each positive integer n we introduce the notion of n-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. We characterize which n-exangulated categories are n-exact in the sense of Jasso and which are (n+2)-angulated in the sense of Geiss-Keller-Oppermann. For extriangulated categories with enough projectives and injectives we introduce the notion of n-cluster tilting subcategories and show that under certain conditions such n-cluster tilting subcategories are n-exangulated.