The aim of this thesis is to develop a localization theory in the higher homological algebra of
n-abelian and n-angulated categories. Analogously to the classical cases of an abelian or a …

Abstract Herschend-Liu-Nakaoka introduced the notion of n-exangulated categories. It is not
only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu …

In this paper, we introduce-abelian and-exact categories by axiomatizing properties of-
cluster tilting subcategories. We study these categories and show that every-cluster tilting …

Xiao and Zhu proved that if C is a locally finite triangulated category, then C has Auslander–
Reiten triangles. Let n be a positive integer. The notion of n-abelian categories is a higher …

Let k be a commutative artinian ring and 𝒜 a small Ext-finite Krull–Schmidt n-abelian k-
category with enough projectives and injectives. We introduce two full subcategories 𝒜 r and …

Let C be an (d+ 2)-angulated category with an d-suspension functor Σd. Our main results
show that every Serre functor on C is an (d+ 2)-angulated functor. We also show that C has a …

Let be a-angulated category with d-suspension functor. Our main results show that every
Serre functor on is a-angulated functor. We also show that has a Serre functor if and only if …

In this article, we introduce the notion of a pre-(n+ 2)-angulated category as a higher
dimensional analogue of a pre-triangulated category defined by Beligiannis-Reiten. We first …

Let A be a finite-dimensional algebra, and M be a d-cluster tilting subcategory of mod A.
From the viewpoint of higher homological algebra, a natural question to ask is when M …

In this paper we introduce $ n\mathbb {Z} $-abelian and $ n\mathbb {Z} $-exact categories
by axiomatising properties of $ n\mathbb {Z} $-cluster tilting subcategories. We study this …