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In n -Exangulated Categories (I), we introduced the notion of n -exangulated categories for each positive integer n. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a common generalization of n -exact categories in the sense of Jasso and (n + 2) -angulated categories in the sense of Geiss-Keller-Oppermann. In this second article we introduce the notion of n -cluster tilting subcategories for extriangulated categories with enough projectives and injectives and show that under certain conditions such n -cluster tilting subcategories are n -exangulated. [ABSTRACT FROM AUTHOR]

Our first aim is to provide an analog of the Gabriel-Quillen embedding theorem for n-exact categories. Also we give an example of an n-exact category that in not an n-cluster tilting subcategory, and we suggest two possible ways for realizing n-exact categories as n-cluster tilting subcategory. [ABSTRACT FROM AUTHOR]

We define the Grothendieck group of an n-exangulated category. For n odd, we show that this group shares many properties with the Grothendieck group of an exact or a triangulated category. In particular, we classify dense complete subcategories of an n-exangulated category with an n-(co)generator in terms of subgroups of the Grothendieck group. This unifies and extends results of Thomason, Bergh–Thaule, Matsui and Zhu–Zhuang for triangulated, (n + 2) -angulated, exact and extriangulated categories, respectively. We also introduce the notion of an n-exangulated subcategory and prove that the subcategories in our classification theorem carry this structure. [ABSTRACT FROM AUTHOR]

We fill a gap in the literature regarding 'transport of structure' for (n + 2) -angulated, n -exact, n -abelian and n -exangulated categories appearing in (classical and higher) homological algebra. As an application of our main results, we show that a skeleton of one of these kinds of categories inherits the same structure in a canonical way, up to equivalence. In particular, it follows that a skeleton of a weak (n + 2) -angulated category is in fact what we call a strong (n + 2) -angulated category. When n = 1 this clarifies a technical concern with the definition of a cluster category. We also introduce the notion of an n -exangulated functor between n -exangulated categories. This recovers the definition of an (n + 2) -angulated functor when the categories concerned are (n + 2) -angulated, and the higher analogue of an exact functor when the categories concerned are n -exact. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An n-exact category is a pair consisting of an additive category and a class of sequences with n + 2 terms satisfying certain axioms. We introduce n-weakly idempotent complete categories. Then we prove that an additive n-weakly idempotent complete category together with the class C n of all contractible sequences with n + 2 terms is an n-exact category. Some properties of the class C n are also discussed. [ABSTRACT FROM AUTHOR]