Exactness of direct limits for abelian categories with an injective cogenerator

0502430 - MÚ 2020 RIV NL eng J - Článek v odborném periodiku
Positselski, Leonid - Šťovíček, J.
Exactness of direct limits for abelian categories with an injective cogenerator.
Journal of Pure and Applied Algebra. Roč. 223, č. 8 (2019), s. 3330-3340. ISSN 0022-4049. E-ISSN 1873-1376
Institucionální podpora: RVO:67985840
Klíčová slova: monads on the category of sets * Grothendieck categories * pure-injectivity
Obor OECD: Pure mathematics
Impakt faktor: 0.770, rok: 2019
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1016/j.jpaa.2018.11.004

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.
Trvalý link: http://hdl.handle.net/11104/0294365