Theorems · Definition · group theory

Representation.Equiv.toLinearEquiv

{A : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [inst : Semiring A] →
          [inst_1 : Monoid G] →
            [inst_2 : AddCommMonoid V] →
              [inst_3 : AddCommMonoid W] →
                [inst_4 : Module A V] →
                  [inst_5 : Module A W] →
                    {ρ : Representation A G V} → {σ : Representation A G W} → ρ.Equiv σ → V ≃ₗ[A] W

Underlying linear isomorphism of an equivalence of representations.

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

10 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Quot.sound

Assumes

SemiringMonoidAddCommMonoidAddCommMonoidModuleModule