{"paper":{"title":"Syntactic Monoids in a Category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.CT"],"primary_cat":"cs.LO","authors_text":"Henning Urbat, Jiri Adamek, Stefan Milius","submitted_at":"2015-04-10T14:44:26Z","abstract_excerpt":"The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott (D = sets), the syntactic semirings of Polak (D = semilattices), and the syntactic associative algebras of Reutenauer (D = vector spaces). Assuming that D is an entropic variety of algebras, we prove that the syntactic D-monoid of a language L can be constructed as a quotient of a free D-monoid modulo the syntactic congruence of L, and tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02694","kind":"arxiv","version":2},"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"}