The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this
paper we introduce the category mo d adm (E) of admissibly finitely presented functors and …

For an exact category E, we study the Butler's condition “AR= Ex”: the relation of the
Grothendieck group of E is generated by Auslander-Reiten conflations. Under some …

Auslander-Reiten duality for module categories is generalised to Grothendieck abelian
categories that have a sufficient supply of finitely presented objects. It is shown that …

Using the Morita-type embedding, we show that any exact category with enough projectives
has a realization as a (pre) resolving subcategory of a module category. When the exact …

Let $\Lambda $ be an artin algebra or, more generally, a locally bounded associative
algebra, and $\mathcal {S}(\Lambda) $ the category of all embeddings $(A\subseteq B) …

Let A be an artin algebra and modA the category of finitely generated A-modules. Unless
stated to the contrary, by a subcategory C of a category we mean a full subcategory of an …

We study elementary Tate objects in an exact category. We characterize the category of
elementary Tate objects as the smallest sub-category of admissible Ind-Pro objects which …

We give a principle in derived categories, which lies behind the classical Auslander–Reiten
duality and its generalized version by Iyama and Wemyss. We apply the principle to show …

In this paper we show that how the representation theory of subcategories (of the category of
modules over an Artin algebra) can be connected to the representation theory of all modules …

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 …