Theorems · Definition · Lie groups

ContIntertwiningMap.comp

{R : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        {U : Type u_5} →
          [inst : Monoid G] →
            [inst_1 : Ring R] →
              [inst_2 : AddCommGroup V] →
                [inst_3 : TopologicalSpace V] →
                  [inst_4 : IsTopologicalAddGroup V] →
                    [inst_5 : Module R V] →
                      [inst_6 : AddCommGroup W] →
                        [inst_7 : TopologicalSpace W] →
                          [inst_8 : IsTopologicalAddGroup W] →
                            [inst_9 : Module R W] →
                              [inst_10 : AddCommGroup U] →
                                [inst_11 : Module R U] →
                                  [inst_12 : TopologicalSpace U] →
                                    [inst_13 : IsTopologicalAddGroup U] →
                                      {π₁ : ContRepresentation R G V} →
                                        {π₂ : ContRepresentation R G W} →
                                          {π₃ : ContRepresentation R G U} →
                                            ContIntertwiningMap π₂ π₃ →
                                              ContIntertwiningMap π₁ π₂ → ContIntertwiningMap π₁ π₃

The composition of two continuous intertwining maps is a continuous intertwining map.

Defined in

Mathlib.RepresentationTheory.Continuous.Basic

Cited by

16 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidRingAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroup