{"paper":{"title":"Birings and plethories of integer-valued polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jesse Elliott","submitted_at":"2011-09-18T06:24:59Z","abstract_excerpt":"Let $A$ and $B$ be commutative rings with identity. An {\\it $A$-$B$-biring} is an $A$-algebra $S$ together with a lift of the functor $Hom_A(S,-)$ from $A$-algebras to sets to a functor from $A$-algebras to $B$-algebras. An {\\it $A$-plethory} is a monoid object in the monoidal category, equipped with the composition product, of $A$-$A$-birings. The polynomial ring $A[X]$ is an initial object in the category of such structures. The $D$-algebra $Int(D)$ has such a structure if $D = A$ is a domain such that the natural $D$-algebra homomorphism $\\theta_n: {\\bigotimes_D}_{i = 1}^n Int(D) \\longright"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3848","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"}