Theorems · Definition · Lie groups

LeftInvariantDerivation.coeFnAddMonoidHom

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_3} →
            [inst_3 : TopologicalSpace H] →
              (I : ModelWithCorners 𝕜 E H) →
                (G : Type u_4) →
                  [inst_4 : TopologicalSpace G] →
                    [inst_5 : ChartedSpace H G] →
                      [inst_6 : Monoid G] →
                        [inst_7 : ContMDiffMul I (↑⊤) G] →
                          LeftInvariantDerivation I G →+
                            ContMDiffMap I (modelWithCornersSelf 𝕜 𝕜) G 𝕜 ↑⊤ →
                              ContMDiffMap I (modelWithCornersSelf 𝕜 𝕜) G 𝕜 ↑⊤

The coercion to function is a monoid homomorphism.

Defined in

Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation

Cited by

1 results in Mathlib

Foundations

Depth 238 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceMonoidContMDiffMul