Auslander's formula and correspondence for exact categories

Abstract

The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category of admissibly finitely presented functors and use it to give a version of Auslander correspondence for any exact category . An important ingredient in the proof is the localization theory of exact categories. We also investigate how properties of are reflected in , for example being (weakly) idempotent complete or having enough projectives or injectives. Furthermore, we describe as a subcategory of when is a resolving subcategory of an abelian category. This includes the category of Gorenstein projective modules and the category of maximal Cohen-Macaulay modules as special cases. Finally, we use to give a bijection between exact structures on an idempotent complete additive category and certain resolving subcategories of .