{"paper":{"title":"The defect recollement, the MacPherson-Vilonen construction, and pp formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Samuel Dean","submitted_at":"2018-08-19T23:06:14Z","abstract_excerpt":"For any abelian category $\\mathcal{A}$, Auslander constructed a localisation $w:\\mathrm{fp}(\\mathcal{A}^{\\mathrm{op}},\\mathrm{Ab})\\to \\mathcal{A}$ called the defect, which is the left adjoint to the Yoneda embedding $Y:\\mathcal{A}\\to\\mathrm{fp}(\\mathcal{A}^{\\mathrm{op}},\\mathrm{Ab})$. If $\\mathcal{A}$ has enough projectives, then this localisation is part of a recollement called the defect recollement. We show that this recollement is an instance of the MacPherson-Vilonen construction if and only if $\\mathcal{A}$ is hereditary. We also discuss several subcategories of $\\mathrm{fp}(\\mathcal{A}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06268","kind":"arxiv","version":4},"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"}