Theorems · Inductive type · group theory

Representation.IntertwiningMap

{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] → Representation A G V → Representation A G W → Type (max u_3 u_4)

An intertwining map between two representations ρ and σ of the same monoid G is a map between underlying modules which commutes with the G-actions.

Defined in

Mathlib.RepresentationTheory.Intertwining

Cited by

261 results in Mathlib

Foundations

Depth 33 from the axioms, rests on 358 definitions · uses propext, Quot.sound

Assumes

SemiringMonoidAddCommMonoidAddCommMonoidModuleModule