The notion of right semi-equivalence in a right (n+ 2)-angulated category is defined in this article. Let C be an n-exangulated category and X is a strongly covariantly finite subcategory of C . We… Expand

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… Expand

We introduce n-abelian and n-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that n-cluster-tilting subcategories of… Expand

We discuss the axioms for an n-angulated category, recently introduced by Geiss, Keller and Op- permann in (2). In particular, we introduce a higher "octahedral axiom", and show that it is equivalent… Expand

Let (C ,E, s) be an extriangulated category. We show that certain quotient categories of extriangulated categories are equivalent to module categories by some restriction of functor E, and in some… Expand

Abstract We define n-angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to… Expand

The notion of D-mutation pairs of subcategories in an n-exangulated category is defined in this article. When (Ƶ, Ƶ) is a D-mutation pair in an n-exangulated category (C, (C,E,s)), the quotient cat...

We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories.… Expand