Theorems · Theorem · group theory

Representation.IntertwiningMap.coprod_inl_inr

∀ {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},
  (Representation.IntertwiningMap.inl A ρ σ).comp (Representation.IntertwiningMap.fst A ρ σ) +
      (Representation.IntertwiningMap.inr A ρ σ).comp (Representation.IntertwiningMap.snd A ρ σ) =
    Representation.IntertwiningMap.id (ρ.prod σ)

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

SemiringMonoidAddCommMonoidAddCommMonoidModuleModule