Theorems · Definition · global analysis

ContMDiffMap.compLeftAddMonoidHom

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {E' : Type u_3} →
            [inst_3 : NormedAddCommGroup E'] →
              [inst_4 : NormedSpace 𝕜 E'] →
                {H : Type u_4} →
                  [inst_5 : TopologicalSpace H] →
                    (I : ModelWithCorners 𝕜 E H) →
                      {H' : Type u_5} →
                        [inst_6 : TopologicalSpace H'] →
                          {I' : ModelWithCorners 𝕜 E' H'} →
                            (N : Type u_6) →
                              [inst_7 : TopologicalSpace N] →
                                [inst_8 : ChartedSpace H N] →
                                  {E'' : Type u_7} →
                                    [inst_9 : NormedAddCommGroup E''] →
                                      [inst_10 : NormedSpace 𝕜 E''] →
                                        {H'' : Type u_8} →
                                          [inst_11 : TopologicalSpace H''] →
                                            {I'' : ModelWithCorners 𝕜 E'' H''} →
                                              {n : WithTop ℕ∞} →
                                                {G' : Type u_10} →
                                                  [inst_12 : AddMonoid G'] →
                                                    [inst_13 : TopologicalSpace G'] →
                                                      [inst_14 : ChartedSpace H' G'] →
                                                        [inst_15 : ContMDiffAdd I' n G'] →
                                                          {G'' : Type u_11} →
                                                            [inst_16 : AddMonoid G''] →
                                                              [inst_17 : TopologicalSpace G''] →
                                                                [inst_18 : ChartedSpace H'' G''] →
                                                                  [inst_19 : ContMDiffAdd I'' n G''] →
                                                                    (φ : G' →+ G'') →
                                                                      ContMDiff I' I'' n ⇑φ →
                                                                        ContMDiffMap I I' N G' n →+
                                                                          ContMDiffMap I I'' N G'' n

For a manifold N and a C^n homomorphism φ between additive Lie groups G', G'', the 'left-composition-by-φ' group homomorphism from C^n⟮I, N; I', G'⟯ to C^n⟮I, N; I'', G''⟯.

Defined in

Mathlib.Geometry.Manifold.Algebra.SmoothFunctions

Cited by

0 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceAddMonoidTopologicalSpaceChartedSpaceContMDiffAddAddMonoidTopologicalSpaceChartedSpaceContMDiffAdd