{"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/globular-weak-o-categories-as-models-of-a","title":"Globular weak $ω$-categories as models of a type theory","arxiv_id":"2106.04475","date":"2021-06-08","proceeding":null,"authors":["Thibaut Benjamin","Eric Finster","Samuel Mimram"],"abstract":"We study the dependent type theory CaTT, introduced by Finster and Mimram, which presents the theory of weak $\\omega$-categories, following the idea that type theories can be considered as presentations of generalized algebraic theories. Our main contribution is a formal proof that the models of this type theory correspond precisely to weak $\\omega$-categories, as defined by Maltsiniotis, by generalizing a definition proposed by Grothendieck for weak $\\omega$-groupoids: Those are defined as suitable presheaves over a cat-coherator, which is a category encoding structure expected to be found in an $\\omega$-category. This comparison is established by proving the initiality conjecture for the type theory CaTT, in a way which suggests the possible generalization to a nerve theorem for a certain class of dependent type theories","url_abs":"https://arxiv.org/abs/2106.04475v2","url_pdf":"https://arxiv.org/pdf/2106.04475v2.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":"globular-weak-o-categories-as-models-of-a","repo_url":"https://github.com/thibautbenjamin/catt-formalization","is_official":0,"mentioned_in_paper":0,"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}