Theorems · Definition · group theory

FDRep.dualTensorIsoLinHom

{k : Type u} →
  {G : Type v} →
    {V : Type u} →
      [inst : Field k] →
        [inst_1 : Group G] →
          [inst_2 : AddCommGroup V] →
            [inst_3 : Module k V] →
              [inst_4 : FiniteDimensional k V] →
                (ρV : Representation k G V) →
                  (W : FDRep k G) →
                    CategoryTheory.MonoidalCategoryStruct.tensorObj (FDRep.of ρV.dual) W ≅ FDRep.of (ρV.linHom W.ρ)

When V and W are finite-dimensional representations of a group G, the isomorphism dualTensorHomEquiv k V W of vector spaces induces an isomorphism of representations.

Defined in

Mathlib.RepresentationTheory.FDRep

Cited by

2 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldGroupAddCommGroupModuleFiniteDimensional