Addendum to “Direct limits in the heart of a t-structure: The case of a torsion pair” [J. Pure Appl. Algebra 219 (9) (2015) 4117–4143

Abstract

Let G be a Grothendieck category, let t=(T,F) be a torsion pair in G and let (Ut,Wt) be the associated Happel–Reiten–Smalø t-structure in the derived category D(G). We prove that the heart of this t-structure is a Grothendieck category if, and only if, the torsionfree class F is closed under taking direct limits in G.