{"paper":{"title":"Functional distribution monads in functional-analytic contexts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CT","authors_text":"Rory B. B. Lucyshyn-Wright","submitted_at":"2017-01-27T18:55:02Z","abstract_excerpt":"We give a general categorical construction that yields several monads of measures and distributions as special cases, alongside several monads of filters. The construction takes place within a categorical setting for generalized functional analysis, called a $\\textit{functional-analytic context}$, formulated in terms of a given monad or algebraic theory $\\mathcal{T}$ enriched in a closed category $\\mathcal{V}$. By employing the notion of $\\textit{commutant}$ for enriched algebraic theories and monads, we define the $\\textit{functional distribution monad}$ associated to a given functional-analy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08152","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"}