{"paper":{"title":"Finite Abelian algebras are dualizable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Pierre Gillibert","submitted_at":"2015-03-09T19:53:28Z","abstract_excerpt":"A finite algebra $\\bA=\\alg{A;\\cF}$ is \\emph{dualizable} if there exists a discrete topological relational structure $\\BA=\\alg{A;\\cG;\\cT}$, compatible with $\\cF$, such that the canonical evaluation map $e\\_{\\bB}\\colon \\bB\\to \\Hom( \\Hom(\\bB,\\bA),\\BA)$ is an isomorphism for every $\\bB$ in the quasivariety generated by $\\bA$. Here, $e\\_{\\bB}$ is defined by $e\\_{\\bB}(x)(f)=f(x)$ for all $x\\in B$ and all $f\\in \\Hom(\\bB,\\bA)$.\n\nWe prove that, given a finite congruence-modular Abelian algebra $\\bA$, the set of all relations compatible with $\\bA$, up to a certain arity, \\emph{entails} the whole set of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02651","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"}