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Title: Auslander's formula and correspondence for exact categories
Authors: HENRARD, Ruben 
Sondre Kvamme
VAN ROOSMALEN, Adam-Christiaan 
Issue Date: 2020
Status: Early view
Abstract: The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ of admissibly finitely presented functors and use it to give a version of Auslander correspondence for any exact category $\mathcal{E}$. An important ingredient in the proof is the localization theory of exact categories. We also investigate how properties of $\mathcal{E}$ are reflected in $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$, for example being (weakly) idempotent complete or having enough projectives or injectives. Furthermore, we describe $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ as a subcategory of $\operatorname{mod}(\mathcal{E})$ when $\mathcal{E}$ 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 $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ to give a bijection between exact structures on an idempotent complete additive category $\mathcal{C}$ and certain resolving subcategories of $\operatorname{mod}(\mathcal{C})$.
Keywords: Mathematics - Representation Theory
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Category: R2
Type: Research Report
Appears in Collections:Research publications

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