{"paper":{"title":"Applications of the Defect of a Finitely Presented Functor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CT","authors_text":"Jeremy Russell","submitted_at":"2012-10-31T23:26:43Z","abstract_excerpt":"For an abelian category $\\mathcal{A}$, the defect sequence $$0\\longrightarrow F_0\\longrightarrow F\\overset{\\varphi}{\\longrightarrow} \\big(w(F),\\hspace{0.05cm}\\underline{\\ \\ }\\hspace{0.1cm} \\big)\\longrightarrow F_1\\longrightarrow 0$$ of a finitely presented functor is used to establish the CoYoneda Lemma. An application of this result is the $\\textsf{fp}$-dual formula which states that for any covariant finitely presented functor $F$, $F^*\\cong \\big(\\hspace{0.05cm}\\underline{\\ \\ }\\hspace{0.1cm} , w(F)\\big)$. The defect sequence is shown to be isomorphic to both the double dual sequence $$0\\long"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0054","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"}