{"paper":{"title":"Monads and limits in bicategories of circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CT","authors_text":"Fosco Loregian","submitted_at":"2025-01-03T16:21:08Z","abstract_excerpt":"We study monads in the (pseudo-)double category $\\mathbf{KSW}(\\mathcal{K})$ where loose arrows are Mealy automata valued in an ambient monoidal category $\\mathcal{K}$, and the category of tight arrows is $\\mathcal{K}$. Such monads turn out to be elegantly described through instances of semifree bicrossed products (bicrossed products of monoids, in the sense of Zappa-Sz\\'ep-Takeuchi, where one factor is a free monoid). This result which gives an explicit description of the `free monad' double left adjoint to the forgetful functor. (Loose) monad maps are interesting as well, and relate to alread"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01882","kind":"arxiv","version":1},"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/2501.01882/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"}