2026-08-07T13:42:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18391 2024-03-06T11:01:46Z ddc:004 open_access

Formalising Yoneda Ext in Univalent Foundations Flaten, Jarl G. Taxerås homotopy type theory homological algebra Yoneda Ext formalisation Coq Ext groups are fundamental objects from homological algebra which underlie important computations in homotopy theory. We formalise the theory of Yoneda Ext groups [Yoneda, 1954] 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jarl G. Taxerås Flaten 2023 Is Part Of LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITP.2023.16 urn:nbn:de:0030-drops-183911 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.16 eng https://creativecommons.org/licenses/by/4.0/legalcode