{"paper":{"title":"Enriched algebraic theories and monads for a system of arities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.LO"],"primary_cat":"math.CT","authors_text":"Rory B. B. Lucyshyn-Wright","submitted_at":"2015-11-09T22:46:05Z","abstract_excerpt":"Under a minimum of assumptions, we develop in generality the basic theory of universal algebra in a symmetric monoidal closed category $\\mathcal{V}$ with respect to a specified system of arities $j:\\mathcal{J} \\hookrightarrow \\mathcal{V}$. Lawvere's notion of algebraic theory generalizes to this context, resulting in the notion of single-sorted $\\mathcal{V}$-enriched $\\mathcal{J}$-cotensor theory, or $\\mathcal{J}$-theory for short. For suitable choices of $\\mathcal{V}$ and $\\mathcal{J}$, such $\\mathcal{J}$-theories include the enriched algebraic theories of Borceux and Day, the enriched Lawver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02920","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"}