%0 Journal Article
%T Addendum to 'Direct limits in the heart of a t-structure: The case of a torsion pair'
%A Carlos E. Parra
%A Manuel Saor¨ªn
%J Mathematics
%D 2015
%I arXiv
%X 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$\o$ 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 $\mathcal{G}$.
%U http://arxiv.org/abs/1509.00258v1