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http://hdl.handle.net/1942/32745
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DC Field | Value | Language |
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dc.contributor.author | HENRARD, Ruben | - |
dc.contributor.author | Sondre Kvamme | - |
dc.contributor.author | VAN ROOSMALEN, Adam-Christiaan | - |
dc.date.accessioned | 2020-12-01T10:05:25Z | - |
dc.date.available | 2020-12-01T10:05:25Z | - |
dc.date.issued | 2020 | - |
dc.date.submitted | 2020-12-01T09:15:18Z | - |
dc.identifier.citation | ADVANCES IN MATHEMATICS (401) | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/1942/32745 | - |
dc.description.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 $\operatorname{mod}(\mathcal{C})$. | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.subject | Mathematics - Representation Theory | - |
dc.subject | Mathematics - Representation Theory | - |
dc.subject | 18E05, 16G50, 18E35 | - |
dc.subject.other | Mathematics - Representation Theory | - |
dc.title | Auslander's formula and correspondence for exact categories | - |
dc.type | Research Report | - |
dc.identifier.volume | 401 | - |
local.format.pages | 36 | - |
local.bibliographicCitation.jcat | R2 | - |
local.publisher.place | 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA | - |
local.type.refereed | Non-Refereed | - |
local.type.specified | Research Report | - |
dc.identifier.doi | 10.1016/j.aim.2022.108296 | - |
dc.identifier.arxiv | 2011.15107 | - |
dc.identifier.isi | 000793102900002 | - |
dc.identifier.url | http://arxiv.org/abs/2011.15107v1 | - |
dc.identifier.eissn | 1090-2082 | - |
local.provider.type | ArXiv | - |
local.uhasselt.uhpub | yes | - |
local.uhasselt.international | yes | - |
item.accessRights | Restricted Access | - |
item.fullcitation | HENRARD, Ruben; Sondre Kvamme & VAN ROOSMALEN, Adam-Christiaan (2020) Auslander's formula and correspondence for exact categories. In: ADVANCES IN MATHEMATICS (401). | - |
item.contributor | HENRARD, Ruben | - |
item.contributor | Sondre Kvamme | - |
item.contributor | VAN ROOSMALEN, Adam-Christiaan | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2023 | - |
crisitem.journal.issn | 0001-8708 | - |
crisitem.journal.eissn | 1090-2082 | - |
Appears in Collections: | Research publications |
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1-s2.0-S0001870822001128-main.pdf Restricted Access | Published version | 954.09 kB | Adobe PDF | View/Open Request a copy |
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