Strictly atomic modules in definable categories

Prest, Mike

doi:10.5802/art.9

Prest, Mike ¹

¹ Department of Mathematics University of Manchester Manchester M13 9PL (UK)

Annals of Representation Theory, Volume 1 (2024) no. 2, pp. 299-334.

Abstract

If $𝒟$ is a definable category then it may contain no nonzero finitely presented objects but, by a result of Makkai, there is a $lim_{\to}$ -generating set of strictly $𝒟$ -atomic modules in $𝒟$ . These modules share some key properties with finitely presented modules.

We consider these modules in general and then in the case that $𝒟$ is the category of modules of some fixed irrational slope over a tubular algebra.

Received: 2023-01-24
Revised: 2024-02-08
Accepted: 2024-03-08
Published online: 2024-05-31

DOI: 10.5802/art.9

Classification: 03C60, 16D90, 16G20, 18E08, 18E10
Keywords: definable category, Mittag-Leffler module, atomic module, tubular algebra, definable closure

Author's affiliations:

Prest, Mike ¹

¹ Department of Mathematics University of Manchester Manchester M13 9PL (UK)

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Prest, Mike. Strictly atomic modules in definable categories. Annals of Representation Theory, Volume 1 (2024) no. 2, pp. 299-334. doi : 10.5802/art.9. https://art.centre-mersenne.org/articles/10.5802/art.9/

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