Strict Mittag-Leffler conditions and locally split morphisms

Yang, Yanjiong; Yan, Xiaobing

doi:10.21136/cmj.2018.0621-16

Czech.Math.J. 2018

DOI: 10.21136/cmj.2018.0621-16

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Strict Mittag-Leffler conditions and locally split morphisms

Yanjiong Yang

Xiaobing Yan

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

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2021

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Projective Covers of Flat Contramodules

Bazzoni

Positselski

Šťovíček

2021

International Mathematics Research Notices

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We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for $\infty $-strictly flat contramodules of projective dimension not exceeding $1$, using an argument based on the notion of the topological Jacobson radical. Covers and precovers of direct limits of more general classes of objects, both in abelian categories with exact and with nonexact direct limits, are also discussed, with an eye towards the Enochs conjecture about covers and direct limits, using locally split (mono)morphisms as the main technique. In particular, we offer a simple elementary proof of the Enochs conjecture for the left class of an $n$-tilting cotorsion pair in an abelian category with exact direct limits.

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Projective Covers of Flat Contramodules

Bazzoni

Positselski

Šťovíček

2021

International Mathematics Research Notices

View full text Add to dashboard Cite

show abstract

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Strict Mittag-Leffler conditions and locally split morphisms

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Cited by 1 publication

References 17 publications

Projective Covers of Flat Contramodules

Projective Covers of Flat Contramodules

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