We study Auslander-Reiten theory in proper abelian subcategories of triangulated
categories with a Serre functor. To initiate this, we use approximations of a Serre functor to …

In this dissertation, let B be a triangulated category and let D be an extension-closed
subcategory of B. First, we give some new characterizations of an Auslander-Reiten triangle …

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 …

Auslander-Reiten duality for module categories is generalized to some sufficiently nice
subcategories. In particular, our consideration works for $\mathcal {P}^{<\infty}(\Lambda) …

We introduce the concept of maximal orthogonal subcategories over artin algebras and
orders, and develop higher Auslander-Reiten theory on them. Auslander-Reiten theory …

We consider functorially finite subcategories in module categories over Artin algebras. One
main result provides a method, in the setup of bounded derived categories, to compute …

Let A be an Artin algebra. As we know, the construction of the well-known Auslander-Reiten
sequence is based on the natural (A, A)-bimodule A and the induced transpose, where the …

We investigate the structure of certain almost split sequences in $\mathcal {P}(\Lambda) $,
ie, the category of morphisms between projective modules over an Artin algebra $\Lambda …

We introduce a notion of generalized Serre duality on a Hom-finite Krull–Schmidt
triangulated category T. This duality induces the generalized Serre functor on T, which is a …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …