𝜏-tilting theory in abelian categories

Liu, Yu; Zhou, Panyue

doi:10.1090/proc/15919

$\tau$-tilting theory in abelian categories
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by Yu Liu and Panyue Zhou

Proc. Amer. Math. Soc. 150 (2022), 2405-2413

DOI: https://doi.org/10.1090/proc/15919

Published electronically: March 8, 2022

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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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