$tau $-tilting theory in abelian categories

摘要

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.