Theorems · Definition · group theory

Representation.IntertwiningMap.fst

(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.prod σ).IntertwiningMap ρ

The projection of a product representation onto its first component is an intertwining map.

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

8 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Quot.sound

Assumes

SemiringMonoidAddCommMonoidAddCommMonoidModuleModule