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http://hdl.handle.net/1942/42932
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DC Field | Value | Language |
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dc.contributor.author | HENRARD, Ruben | - |
dc.contributor.author | VAN ROOSMALEN, Adam-Christiaan | - |
dc.date.accessioned | 2024-05-14T11:44:56Z | - |
dc.date.available | 2024-05-14T11:44:56Z | - |
dc.date.issued | 2024 | - |
dc.date.submitted | 2024-05-13T08:36:52Z | - |
dc.identifier.citation | JOURNAL OF PURE AND APPLIED ALGEBRA, 228 (7) (Art N° 107635) | - |
dc.identifier.uri | http://hdl.handle.net/1942/42932 | - |
dc.description.abstract | One-sided exact categories are obtained via a weakening of a Quillen exact category. Such one-sided exact categories are homologically similar to Quillen exact categories: a one-sided exact category E can be (essentially uniquely) embedded into its exact hull Eex; this embedding induces a derived equivalence Db(E) -> Db(Eex). Whereas it is well known that Quillen's obscure axioms are redundant for exact categories, some one-sided exact categories are known to not satisfy the corresponding obscure axiom. In fact, we show that the failure of the obscure axiom is controlled by the embedding of E into its exact hull Eex or, equivalently, into its derived category Db(E). We introduce three versions of the obscure axiom (these versions coincide when the category is weakly idempotent complete) and establish equivalent homological properties, such as the snake lemma and the nine lemma. We show that a one-sided exact category admits a closure under each of these obscure axioms, each of which preserves the bounded derived category up to triangle equivalence. (c) 2024 Elsevier B.V. All rights reserved. | - |
dc.language.iso | en | - |
dc.publisher | ELSEVIER | - |
dc.rights | 2024 Elsevier B.V. | - |
dc.subject.other | Exact category | - |
dc.subject.other | Homological algebra | - |
dc.subject.other | Derived category | - |
dc.subject.other | Weak idempotent completion | - |
dc.title | On the obscure axiom for one-sided exact categories | - |
dc.type | Journal Contribution | - |
dc.identifier.issue | 7 | - |
dc.identifier.volume | 228 | - |
local.format.pages | 37 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | van Roosmalen, AC (corresponding author), Xian Jiaotong Liverpool Univ, Dept Pure Math, Suzhou 215123, Peoples R China. | - |
dc.description.notes | ruben.henrard@uhasselt.be; ac.vanroosmalen@xjtlu.edu.cn | - |
local.publisher.place | RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
local.bibliographicCitation.artnr | 107635 | - |
dc.identifier.doi | 10.1016/j.jpaa.2024.107635 | - |
dc.identifier.isi | 001198977200001 | - |
local.provider.type | wosris | - |
local.description.affiliation | [Henrard, Ruben] Univ Hasselt, Dept WNI, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. | - |
local.description.affiliation | [van Roosmalen, Adam-Christiaan] Xian Jiaotong Liverpool Univ, Dept Pure Math, Suzhou 215123, Peoples R China. | - |
local.uhasselt.international | yes | - |
item.accessRights | Restricted Access | - |
item.contributor | HENRARD, Ruben | - |
item.contributor | VAN ROOSMALEN, Adam-Christiaan | - |
item.fulltext | With Fulltext | - |
item.fullcitation | HENRARD, Ruben & VAN ROOSMALEN, Adam-Christiaan (2024) On the obscure axiom for one-sided exact categories. In: JOURNAL OF PURE AND APPLIED ALGEBRA, 228 (7) (Art N° 107635). | - |
crisitem.journal.issn | 0022-4049 | - |
crisitem.journal.eissn | 1873-1376 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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On the obscure axiom for one-sided exact categories.pdf Restricted Access | Published version | 9.99 MB | Adobe PDF | View/Open Request a copy |
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