Publication detail
Cofibrant generation of pure monomorphisms
LIEBERMAN, M. POSITSELSKI, L. ROSICKÝ, J. VASEY, S.
English title
Cofibrant generation of pure monomorphisms
Type
journal article in Web of Science
Language
en
Original abstract
We show that pure monomorphisms are cofibrantly generated-generated from a set of morphisms by pushouts, transfinite composition, and retracts-in any locally finitely presentable additive category. In particular, this is true in any category of R-modules. On the other hand, the classes of all monomorphisms and regular monomorphisms in a locally finitely presentable additive category need not be well-behaved. (C) 2020 Elsevier Inc. All rights reserved.
English abstract
We show that pure monomorphisms are cofibrantly generated-generated from a set of morphisms by pushouts, transfinite composition, and retracts-in any locally finitely presentable additive category. In particular, this is true in any category of R-modules. On the other hand, the classes of all monomorphisms and regular monomorphisms in a locally finitely presentable additive category need not be well-behaved. (C) 2020 Elsevier Inc. All rights reserved.
Keywords in English
Pure monomorphism, pure injective, cofibrant generation, locally finitely presentable category, additive category
Released
15.10.2020
Publisher
Elsevier
Location
Amsterdam, Netherlands
ISSN
0021-8693
Volume
560
Pages from–to
1297–1310
Pages count
14
BIBTEX
@article{BUT164387,
author="Michael Joseph {Lieberman} and Leonid {Positselski} and Jiří {Rosický} and Sebastien {Vasey},
title="Cofibrant generation of pure monomorphisms",
year="2020",
volume="560",
month="October",
pages="1297--1310",
publisher="Elsevier",
address="Amsterdam, Netherlands",
issn="0021-8693"
}