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@aljungstrom aljungstrom commented Nov 15, 2024

This PR looks very big but I swear it isn't that bad... It contains:

  • Main result: (appropriate versions of) bilinearity, 'graded' commutativity and the Jacobi identity for generalised Whitehead products. These are found in Cubical.Homotopy.WhiteheadProducts.Generalised.* for generalised whitehead products (both defined in terms of smash products and joins) and in Cubical.Homotopy.WhiteheadProducts.Properties for the standard non-generalised version.

A bunch of results needed for the above, including:

  • Some stuff about even/odd numbers in Cubical.Data.Nat.IsEven and an "isEven solver" in Cubical.Tactics.EvenOddSolver
  • Co-H-Space structure on joins in Cubical.HITs.Join.CoHSpace.
  • Lemmas about iterated involutions
  • added biimplication to Cubical.Foundations.Prelude. Felt reasonable to have...
  • Some other cute lemmas here and there...

@aljungstrom aljungstrom marked this pull request as draft November 15, 2024 01:34
@aljungstrom aljungstrom changed the title Lie algebra properties of generalised whitehead products Lie algebra properties of generalised Whitehead products Nov 15, 2024
@aljungstrom aljungstrom marked this pull request as ready for review September 25, 2025 13:05
@aljungstrom aljungstrom changed the title Lie algebra properties of generalised Whitehead products Lie algebra properties of Whitehead products Sep 26, 2025
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