Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/32745
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dc.contributor.authorHENRARD, Ruben-
dc.contributor.authorSondre Kvamme-
dc.contributor.authorVAN ROOSMALEN, Adam-Christiaan-
dc.date.accessioned2020-12-01T10:05:25Z-
dc.date.available2020-12-01T10:05:25Z-
dc.date.issued2020-
dc.date.submitted2020-12-01T09:15:18Z-
dc.identifier.citationADVANCES IN MATHEMATICS (401)-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/1942/32745-
dc.description.abstractThe 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 $\operatorname{mod}(\mathcal{C})$.-
dc.language.isoen-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.subjectMathematics - Representation Theory-
dc.subjectMathematics - Representation Theory-
dc.subject18E05, 16G50, 18E35-
dc.subject.otherMathematics - Representation Theory-
dc.titleAuslander's formula and correspondence for exact categories-
dc.typeResearch Report-
dc.identifier.volume401-
local.format.pages36-
local.bibliographicCitation.jcatR2-
local.publisher.place525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA-
local.type.refereedNon-Refereed-
local.type.specifiedResearch Report-
dc.identifier.doi10.1016/j.aim.2022.108296-
dc.identifier.arxiv2011.15107-
dc.identifier.isi000793102900002-
dc.identifier.urlhttp://arxiv.org/abs/2011.15107v1-
dc.identifier.eissn1090-2082-
local.provider.typeArXiv-
local.uhasselt.uhpubyes-
local.uhasselt.internationalyes-
item.accessRightsRestricted Access-
item.fullcitationHENRARD, Ruben; Sondre Kvamme & VAN ROOSMALEN, Adam-Christiaan (2020) Auslander's formula and correspondence for exact categories. In: ADVANCES IN MATHEMATICS (401).-
item.fulltextWith Fulltext-
crisitem.journal.issn0001-8708-
crisitem.journal.eissn1090-2082-
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