Group Cohomology in the Lean Community Library

Author Amelia Livingston

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Amelia Livingston
  • King’s College London, UK


I am very grateful to Kevin Buzzard for his ongoing mathematical and Lean-related support and guidance. I am also indebted to Joël Riou for his explanation of the simplicial interpretation of group cohomology and his thorough reviewing of and advice regarding my work, and for his formalisation of some of the results I used. I also depended heavily on Scott Morrison’s development of Lean’s representation theory library and the category theory library more generally. Finally, thanks to anyone who answered my questions on the Xena Project Discord server and the Lean Zulip.

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Amelia Livingston. Group Cohomology in the Lean Community Library. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Group cohomology is a tool which has become indispensable in a wide range of modern mathematics, like algebraic geometry and algebraic number theory, as well as group theory itself. For example, it allows us to reformulate classical class field theory in cohomological terms; this formulation is essential to landmarks of modern number theory, like Wiles’s proof of Fermat’s Last Theorem. We explore the challenges of formalising group cohomology in the Lean theorem prover in a generality suitable for inclusion in the community library mathlib.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Type theory
  • formal math
  • Lean
  • mathlib
  • group cohomology
  • homological algebra


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