Strictly atomic modules in definable categories

Abstract

If $\mathcal{D}$ is a definable category then it may contain no nonzero finitely presented modules but, by a result of Makkai, there is a $\underrightarrow{\lim }$-generating set of strictly $\mathcal{D}$-atomic modules. These modules share some key properties of finitely presented modules. We consider these modules in general and then in the case that $\mathcal{D}$ is the category of modules of some fixed irrational slope over a tubular algebra.

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