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arXiv · 1805.05156

Exactness of direct limits for abelian categories with an injective cogenerator

Leonid Positselski·Jan Stovicek
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Abstract

We prove that the exactness of direct limits in an abelian category with products and an injective cogenerator J is equivalent to a condition on J which is well-known to characterize pure-injectivity in module categories, and we describe an application of this result to the tilting theory. We derive our result as a consequence of a more general characterization of when inverse limits in the Eilenberg-Moore category of a monad on the category of sets preserve regular epimorphisms.

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Leonid Positselski, Jan Stovicek. 2018-05-14. Exactness of direct limits for abelian categories with an injective cogenerator. https://doi.org/10.1016/j.jpaa.2018.11.004

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