For large classes of Grothendieck categories, the heart of the Happel-Reiten-Smaloe t-structure is locally finitely presented exactly when the torsion pair is generated by finitely presented objects.
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Locally finitely presented and coherent hearts
For large classes of Grothendieck categories, the heart of the Happel-Reiten-Smaloe t-structure is locally finitely presented exactly when the torsion pair is generated by finitely presented objects.