Theorems · Definition · Lie groups

ContIntertwiningMap.toIntertwiningMap

{R : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [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] →
                            {π₁ : ContRepresentation R G V} →
                              {π₂ : ContRepresentation R G W} →
                                ContIntertwiningMap π₁ π₂ →
                                  (ContRepresentation.toRepresentation R G V π₁).IntertwiningMap
                                    (ContRepresentation.toRepresentation R G W π₂)

Any continuous intertwining map is an intertwining map.

Defined in

Mathlib.RepresentationTheory.Continuous.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

MonoidRingAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleAddCommGroupTopologicalSpaceIsTopologicalAddGroupModule