Strictly atomic modules in definable categories
Prest, Mike1
1 Department of Mathematics University of Manchester Manchester M13 9PL (UK)
Annals of Representation Theory, Volume 1 (2024) no. 2, pp. 299-334.

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 →-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:
Revised:
Accepted:
Published online:
DOI: 10.5802/art.9
Classification: 03C60, 16D90, 16G20, 18E08, 18E10
Keywords: definable category, Mittag-Leffler module, atomic module, tubular algebra, definable closure
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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