Auslander's formula and correspondence for exact categories
Peer reviewed, Journal article
Published version
Date
2022Metadata
Show full item recordCollections
- Institutt for matematiske fag [2527]
- Publikasjoner fra CRIStin - NTNU [38679]
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 .