Auslander's formula and correspondence for exact categories

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 version for any exact E. An important ingredient proof localization theory categories. We also investigate how properties E are reflected modadm(E), example being (weakly) idempotent complete or having enough projectives injectives. Furthermore, describe as subcategory mod(E) when resolving an abelian category. This includes Gorenstein projective modules maximal Cohen-Macaulay special cases. Finally, bijection between structures on additive C certain subcategories mod(C).