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arXiv · 2010.14869

$\tau$-tilting theory in abelian categories

Yu Liu·Panyue Zhou
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Abstract

Let $\mathcal A$ be a Hom-finite abelian category with enough projectives. In this note, we show that any covariantly finite $\tau$-rigid subcategory is contained in a support $\tau$-tilting subcategory. We also show that support $\tau$-tilting subcategories are in bijection with certain finitely generated torsion classes. Some applications of our main results are also given.

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Yu Liu, Panyue Zhou. 2020-10-28. $\tau$-tilting theory in abelian categories. https://arxiv.org/abs/2010.14869

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