{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-semibicategory-of-moore-automata","title":"The semibicategory of Moore automata","arxiv_id":"2305.00272","date":"2023-04-29","proceeding":null,"authors":["Guido Boccali","Bojana Femić","Andrea Laretto","Fosco Loregian","Stefano Luneia"],"abstract":"We study the semibicategory $\\textsf{Mre}$ of \"Moore automata\": an arrangement of objects, 1- and 2-cells which is inherently and irredeemably nonunital in dimension one. Between the semibicategory of Moore automata and the better behaved bicategory $\\textsf{Mly}$ of \"Mealy automata\" a plethora of adjunctions insist: the well-known essential equivalence between the two kinds of state machines that model the definitions of $\\textsf{Mre}$ and $\\textsf{Mly}$ is appreciated at the categorical level, as the equivalence induced between the fixpoints of an adjunction, in fact exhibiting $\\textsf{Mre}(A,B)$ as a coreflective subcategory of $\\textsf{Mly}(A,B)$; the comodality induced by this adjunction is but the $0$th step of a `level-like' filtration of the bicategory $\\textsf{Mre}$ in a countable family of essential bi-localizations $\\textsf{s}^n\\textsf{Mre}\\subseteq\\textsf{Mre}$. We outline a way to generate intrinsically meaningful adjunctions of this form. We mechanize some of our main results using the proof assistant Agda.","url_abs":"https://arxiv.org/abs/2305.00272v1","url_pdf":"https://arxiv.org/pdf/2305.00272v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-semibicategory-of-moore-automata","repo_url":"https://github.com/iwilare/categorical-automata","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}