Auslander's formula and correspondence for exact categories

Ruben Henrard, Sondre Kvamme, Adam Christiaan van Roosmalen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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

Original languageEnglish
Article number108296
JournalAdvances in Mathematics
Publication statusPublished - 4 Jun 2022
Externally publishedYes


  • Auslander correspondence
  • Effaceable functor
  • Exact category
  • Resolving subcategory


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