{"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/completeness-for-categories-of-generalized","title":"Completeness for categories of generalized automata","arxiv_id":"2303.03867","date":"2023-03-07","proceeding":null,"authors":["Guido Boccali","Andrea Laretto","Fosco Loregian","Stefano Luneia"],"abstract":"We present a slick proof of completeness and cocompleteness for categories of $F$-automata, where the span of maps $E\\leftarrow E\\otimes I \\to O$ that usually defines a deterministic automaton of input $I$ and output $O$ in a monoidal category $(\\mathcal K,\\otimes)$ is replaced by a span $E\\leftarrow F E \\to O$ for a generic endofunctor $F : \\mathcal K\\to \\mathcal K$ of a generic category $\\mathcal K$: these automata exist in their `Mealy' and `Moore' version and form categories $F\\text{-}\\mathsf{Mly}$ and $F\\text{-}\\mathsf{Mre}$; such categories can be presented as strict 2-pullbacks in $\\mathsf{Cat}$ and whenever $F$ is a left adjoint, both $F\\text{-}\\mathsf{Mly}$ and $F\\text{-}\\mathsf{Mre}$ admit all limits and colimits that $\\mathcal K$ admits. We mechanize some of of our main results using the proof assistant Agda and the library `agda-categories`.","url_abs":"https://arxiv.org/abs/2303.03867v1","url_pdf":"https://arxiv.org/pdf/2303.03867v1.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":"completeness-for-categories-of-generalized","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":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}