Theorems · Definition · group theory

Subrepresentation.subrepresentationSubmoduleOrderIso

{A : Type u_1} →
  {G : Type u_2} →
    {W : Type u_3} →
      [inst : CommSemiring A] →
        [inst_1 : Monoid G] →
          [inst_2 : AddCommMonoid W] →
            [inst_3 : Module A W] →
              {ρ : Representation A G W} → Subrepresentation ρ ≃o Submodule (MonoidAlgebra A G) ρ.asModule

An order-preserving equivalence between subrepresentations of ρ and submodules of ρ.asModule.

Defined in

Mathlib.RepresentationTheory.Subrepresentation

Cited by

4 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule