{"paper":{"title":"Duality and contravariant functors in the representation theory of artin algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.LO"],"primary_cat":"math.RT","authors_text":"Samuel Dean","submitted_at":"2016-03-18T13:01:13Z","abstract_excerpt":"We know that the model theory of modules leads to a way of obtaining definable categories of modules over a ring $R$ as the kernels of certain functors $(R\\textbf{-Mod})^{\\text{op}}\\to\\textbf{Ab}$ rather than of functors $R\\textbf{-Mod}\\to\\textbf{Ab}$ which are given by a pp pair. This paper will give various algebraic characterisations of these functors in the case that $R$ is an artin algebra.\n  Suppose that $R$ is an artin algebra. An additive functor $G:(R\\textbf{-Mod})^{\\text{op}}\\to\\textbf{Ab}$ preserves inverse limits and $G|_{(R\\textbf{-mod})^{\\text{op}}}:(R\\textbf{-mod})^{\\text{op}}\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05863","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"}