{"paper":{"title":"Epireflective subcategories and formal closure operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Marino Gran, Mathieu Duckerts-Antoine, Zurab Janelidze","submitted_at":"2016-05-27T13:20:01Z","abstract_excerpt":"On a category $\\mathscr{C}$ with a designated (well-behaved) class $\\mathcal{M}$ of monomorphisms, a closure operator in the sense of D. Dikranjan and E. Giuli is a pointed endofunctor of $\\mathcal{M}$, seen as a full subcategory of the arrow-category $\\mathscr{C}^\\mathbf{2}$ whose objects are morphisms from the class $\\mathcal{M}$, which \"commutes\" with the codomain functor $\\mathsf{cod}\\colon \\mathcal{M}\\to \\mathscr{C}$. In other words, a closure operator consists of a functor $C\\colon \\mathcal{M}\\to\\mathcal{M}$ and a natural transformation $c\\colon 1_\\mathcal{M}\\to C$ such that $\\mathsf{cod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08627","kind":"arxiv","version":3},"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"}