Theorems · Theorem · group theory

Representation.TensorProduct.comm_comp_rTensor

∀ {A : Type u_1} {G : Type u_2} {V : Type u_3} {W : Type u_4} {U : Type u_5} [inst : CommSemiring A] [inst_1 : Monoid G]
  [inst_2 : AddCommMonoid V] [inst_3 : AddCommMonoid W] [inst_4 : AddCommMonoid U] [inst_5 : Module A V]
  [inst_6 : Module A W] [inst_7 : Module A U] (ρ : Representation A G V) (σ : Representation A G W)
  (τ : Representation A G U) (f : σ.IntertwiningMap τ),
  (↑(Representation.TensorProduct.comm τ ρ)).comp (Representation.IntertwiningMap.rTensor ρ f) =
    (Representation.IntertwiningMap.lTensor ρ f).comp ↑(Representation.TensorProduct.comm σ ρ)

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule