Theorems · Definition · global analysis

smoothSheafCommGroup.compLeft

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {EM : Type u_2} →
      [inst_1 : NormedAddCommGroup EM] →
        [inst_2 : NormedSpace 𝕜 EM] →
          {HM : Type u_3} →
            [inst_3 : TopologicalSpace HM] →
              (IM : ModelWithCorners 𝕜 EM HM) →
                {E : Type u_4} →
                  [inst_4 : NormedAddCommGroup E] →
                    [inst_5 : NormedSpace 𝕜 E] →
                      {H : Type u_5} →
                        [inst_6 : TopologicalSpace H] →
                          (I : ModelWithCorners 𝕜 E H) →
                            {H' : Type u_6} →
                              [inst_7 : TopologicalSpace H'] →
                                (I' : ModelWithCorners 𝕜 E H') →
                                  (M : Type u) →
                                    [inst_8 : TopologicalSpace M] →
                                      [inst_9 : ChartedSpace HM M] →
                                        (A A' : Type u) →
                                          [inst_10 : TopologicalSpace A] →
                                            [inst_11 : ChartedSpace H A] →
                                              [inst_12 : TopologicalSpace A'] →
                                                [inst_13 : ChartedSpace H' A'] →
                                                  [inst_14 : CommGroup A] →
                                                    [inst_15 : CommGroup A'] →
                                                      [inst_16 : LieGroup I (↑⊤) A] →
                                                        [inst_17 : LieGroup I' (↑⊤) A'] →
                                                          (φ : A →* A') →
                                                            ContMDiff I I' ↑⊤ ⇑φ →
                                                              (smoothSheafCommGroup IM I M A ⟶
                                                                smoothSheafCommGroup IM I' M A')

For a manifold M and a smooth homomorphism φ between abelian Lie groups A, A', the 'left-composition-by-φ' morphism of sheaves from smoothSheafCommGroup IM I M A to smoothSheafCommGroup IM I' M A'.

Defined in

Mathlib.Geometry.Manifold.Sheaf.Smooth

Cited by

0 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceCommGroupCommGroupLieGroupLieGroup