{"paper":{"title":"Addendum to 'Direct limits in the heart of a t-structure: The case of a torsion pair'","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Carlos E. Parra, Manuel Saor\\'in","submitted_at":"2015-09-01T12:33:25Z","abstract_excerpt":"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 $\\mathcal{G}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00258","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}