Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
$\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ 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
$\operatorname{mod}(\mathcal{C})$.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: atom-ph