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http://hdl.handle.net/1942/40277
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DC Field | Value | Language |
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dc.contributor.author | HENRARD, Ruben | - |
dc.contributor.author | Kvamme, Sondre | - |
dc.contributor.author | VAN ROOSMALEN, Adam-Christiaan | - |
dc.contributor.author | Wegner, Sven-Ake | - |
dc.date.accessioned | 2023-06-05T09:38:25Z | - |
dc.date.available | 2023-06-05T09:38:25Z | - |
dc.date.issued | 2023 | - |
dc.date.submitted | 2023-06-02T14:12:10Z | - |
dc.identifier.citation | REVISTA MATEMATICA IBEROAMERICANA, 39 (2) , p. 439 -494 | - |
dc.identifier.uri | http://hdl.handle.net/1942/40277 | - |
dc.description.abstract | Quasi-abelian categories are abundant in functional analysis and repre-sentation theory. It is known that a quasi-abelian category 8 is a cotilting torsionfree class of an abelian category. In fact, this property characterizes quasi-abelian cate-gories. This ambient abelian category is derived equivalent to the category 8, and can be constructed as the heart ZJe (8) of a t-structure on the bounded derived cate-gory Db(8) or as the localization of the category of monomorphisms in 8. However, there are natural examples of categories in functional analysis which are not quasi-abelian, but merely one-sided quasi-abelian or even weaker. Examples are the category of LB-spaces or the category of complete Hausdorff locally convex spaces. In this paper, we consider additive regular categories as a generalization of quasi-abelian categories that covers the aforementioned examples. Additive regular categories can be characterized as those subcategories of abelian categories which are closed under subobjects. As for quasi-abelian categories, we show that such an ambient abelian category of an additive regular category 8 can be found as the heart of a t-structure on the bounded derived category Db(8), or as the localization of the category of monomor-phisms of 8. In our proof of this last construction, we formulate and prove a version of Auslander's formula for additive regular categories. Whereas a quasi-abelian category is an exact category in a natural way, an addi-tive regular category has a natural one-sided exact structure. Such a one-sided exact category can be 2-universally embedded into its exact hull. We show that the exact hull of an additive regular category is again an additive regular category. | - |
dc.description.sponsorship | The third author gratefully acknowledges the support received from the Research Foundation-Flanders (FWO), 12.M33.16N The authors thank Luisa Fiorot and Michel Van den Bergh for helpful discussions. The second author would like to thank the Hausdorff Institute for Mathematics in Bonn, since parts of the paper were written during his stay at the junior trimester program ”New Trends in Representation Theory”. | - |
dc.language.iso | en | - |
dc.publisher | EUROPEAN MATHEMATICAL SOC-EMS | - |
dc.rights | 2022 Real Sociedad Matemática Española Published by EMS Press and licensed under a CC BY 4.0 license Open access | - |
dc.subject.other | Exact category | - |
dc.subject.other | regular category | - |
dc.subject.other | t-structure | - |
dc.title | The left heart and exact hull of an additive regular category | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 494 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 439 | - |
dc.identifier.volume | 39 | - |
local.format.pages | 56 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Henrard, R (corresponding author), Hasselt Univ, Dept WNI, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. | - |
dc.description.notes | ruben.henrard@ahasselt.be; sondre.kvamme@ntnu.no; | - |
dc.description.notes | ae.vanroosmalen@xith.edu.cn; sven.wegner@hamburge.de | - |
local.publisher.place | PUBLISHING HOUSE GMBH INST MATHEMATIK TECHNISCHE UNIV BERLIN STRASSE 17, JUNI 136, BERLIN, 10623, GERMANY | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.4171/RMI/1388 | - |
dc.identifier.isi | 000982518200002 | - |
dc.identifier.eissn | - | |
local.provider.type | wosris | - |
local.description.affiliation | [Henrard, Ruben] Hasselt Univ, Dept WNI, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. | - |
local.description.affiliation | [Kvamme, Sondre] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway. | - |
local.description.affiliation | [van Roosmalen, Adam-Christiaan] Xian Jiaotong Liverpool Univ, Dept Pure Math, Suzhou 215123, Peoples R China. | - |
local.description.affiliation | [Wegner, Sven-Ake] Univ Hamburg, Dept Math, Bundesstr 55, D-20146 Hamburg, Germany. | - |
local.uhasselt.international | yes | - |
item.contributor | HENRARD, Ruben | - |
item.contributor | Kvamme, Sondre | - |
item.contributor | VAN ROOSMALEN, Adam-Christiaan | - |
item.contributor | Wegner, Sven-Ake | - |
item.accessRights | Open Access | - |
item.fulltext | With Fulltext | - |
item.fullcitation | HENRARD, Ruben; Kvamme, Sondre; VAN ROOSMALEN, Adam-Christiaan & Wegner, Sven-Ake (2023) The left heart and exact hull of an additive regular category. In: REVISTA MATEMATICA IBEROAMERICANA, 39 (2) , p. 439 -494. | - |
crisitem.journal.issn | 0213-2230 | - |
Appears in Collections: | Research publications |
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27572.pdf | Published version | 984.41 kB | Adobe PDF | View/Open |
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