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Addendum to “Direct limits in the heart of a t-structure: the case of a torsion pair”. (English) Zbl 1397.18027
Summary: 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-Smalø 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 $$\mathcal{G}$$.
Addendum to the authors’ paper [ibid. 219, No. 9, 4117–4143 (2015; Zbl 1333.18017)].

##### MSC:
 1.8e+31 Derived categories, triangulated categories (MSC2010) 1.8e+16 Grothendieck categories (MSC2010) 1.8e+41 Torsion theories, radicals 1.6e+06 Syzygies, resolutions, complexes in associative algebras 1.6e+31 Homological functors on modules (Tor, Ext, etc.) in associative algebras
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