{"paper":{"title":"Commutants for enriched algebraic theories and monads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Rory B. B. Lucyshyn-Wright","submitted_at":"2016-04-28T19:39:27Z","abstract_excerpt":"We define and study a notion of $\\textit{commutant}$ for $\\mathcal{V}$-enriched $\\mathcal{J}$-algebraic theories for a system of arities $\\mathcal{J}$, recovering the usual notion of commutant or centralizer of a subring as a special case alongside Wraith's notion of commutant for Lawvere theories as well as a notion of commutant for $\\mathcal{V}$-monads on a symmetric monoidal closed category $\\mathcal{V}$. This entails a thorough study of commutation and Kronecker products of operations in $\\mathcal{J}$-theories. In view of the equivalence between $\\mathcal{J}$-theories and $\\mathcal{J}$-ary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08569","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"}