Addendum to 'Direct limits in the heart of a t-structure: The case of a torsion pair'

Abstract

Let $\mathcal{G}$ be a Grothendieck category, let $\mathbf{t}=(\mathcal{T},\mathcal{F})$ be a torsion pair in $\mathcal{G}$ and let $({\mathcal{U}}_{\mathbf{t}},{\mathcal{W}}_{\mathbf{t}})$ be the associated Happel-Reiten-Smal$ø$ t-structure in the derived category $\mathcal{D}(\mathcal{G})$. We prove that the heart of this t-structure is a Grothendieck category if, and only if, the torsionfree class $\mathcal{F}$ is closed under taking direct limits in $\mathcal{G}$.

Cited by in corpus (2)

• On locally coherent hearts
• Hearts for commutative noetherian rings: torsion pairs and derived equivalences