Locally coherent exact categories
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00588518" target="_blank" >RIV/67985840:_____/24:00588518 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10485-024-09780-1" target="_blank" >https://doi.org/10.1007/s10485-024-09780-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10485-024-09780-1" target="_blank" >10.1007/s10485-024-09780-1</a>
Alternative languages
Result language
angličtina
Original language name
Locally coherent exact categories
Original language description
A locally coherent exact category is a finitely accessible additive category endowed with an exact structure in which the admissible short exact sequences are the directed colimits of admissible short exact sequences of finitely presentable objects. We show that any exact structure on a small idempotent-complete additive category extends uniquely to a locally coherent exact structure on the category of ind-objects, in particular, any finitely accessible category has the unique maximal and the unique minimal locally coherent exact category structures. All locally coherent exact categories are of Grothendieck type in the sense of Št’ovíček. We also discuss the canonical embedding of a small exact category into the abelian category of additive sheaves in connection with the locally coherent exact structure on the ind-objects, and deduce two periodicity theorems as applications.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA23-05148S" target="_blank" >GA23-05148S: Homological and structural theory in geometric contexts</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Categorical Structures
ISSN
0927-2852
e-ISSN
1572-9095
Volume of the periodical
32
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
30
Pages from-to
20
UT code for WoS article
001277796100001
EID of the result in the Scopus database
2-s2.0-85199810565