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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:
18E30 Derived categories, triangulated categories (MSC2010)
18E15 Grothendieck categories (MSC2010)
18E40 Torsion theories, radicals
16E05 Syzygies, resolutions, complexes in associative algebras
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
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