{"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/formalising-yoneda-ext-in-univalent","title":"Formalising Yoneda Ext in Univalent Foundations","arxiv_id":"2302.12678","date":"2023-02-24","proceeding":null,"authors":["Jarl G. Taxerås Flaten"],"abstract":"Ext groups are fundamental objects from homological algebra which underlie important computations in homotopy theory. We formalise the theory of Yoneda Ext groups in homotopy type theory (HoTT) using the Coq-HoTT library. This is an approach to Ext which does not require projective or injective resolutions, though it produces large abelian groups. Using univalence, we show how these Ext groups can be naturally represented in HoTT. We give a novel proof and formalisation of the usual six-term exact sequence via a fibre sequence of 1-types (or groupoids), along with an application. In addition, we discuss our formalisation of the contravariant long exact sequence of Ext, an important computational tool. Along the way we implement and explain the Baer sum of extensions and how Ext is a bifunctor.","url_abs":"https://arxiv.org/abs/2302.12678v2","url_pdf":"https://arxiv.org/pdf/2302.12678v2.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":"formalising-yoneda-ext-in-univalent","repo_url":"https://github.com/jarlg/Yoneda-Ext","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}