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"
}