{"paper":{"title":"Two-dimensional transducers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Fosco Loregian","submitted_at":"2025-09-08T14:53:31Z","abstract_excerpt":"We define a bicategory $\\mathbf{2TDX}$ whose 1-cells provide a categorification of transducers, computational devices extending finite-state automata with output capabilities. This bicategory is a mathematically interesting object: its objects are categories $\\mathcal{A},\\mathcal{B},\\dots$ and its 1-cells $(\\mathcal{Q}, t) : \\mathcal{A} \\to \\mathcal{B}$ consist of a category $\\mathcal{Q}$ of `states', and a profunctor $$ t : \\mathcal{A} \\times \\mathcal{Q}^\\text{op}\\times\\mathcal{Q} \\times (\\mathcal{B}^*)^\\text{op} \\to \\mathbf{Set} $$ where $\\mathcal{B}^*$ denotes the free monoidal category ove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06769","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.06769/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}