Exactness of direct limits for abelian categories with an injective cogenerator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00502430" target="_blank" >RIV/67985840:_____/19:00502430 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/19:10400304
Result on the web
<a href="http://dx.doi.org/10.1016/j.jpaa.2018.11.004" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2018.11.004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2018.11.004" target="_blank" >10.1016/j.jpaa.2018.11.004</a>

Result language
angličtina
Original language name
Exactness of direct limits for abelian categories with an injective cogenerator
Original language description
We prove that the exactness of direct limits in an abelian category with products and an injective cogenerator J is equivalent to a condition on J which is well-known to characterize pure-injectivity in module categories, and we describe an application of this result to the tilting theory. We derive our result as a consequence of a more general characterization of when inverse limits in the Eilenberg–Moore category of a monad on the category of sets preserve regular epimorphisms.
Czech name
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Czech description
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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

Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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