Theorems · Definition · group theory

Subrepresentation.submoduleSubrepresentationOrderIso

{A : Type u_1} →
  {G : Type u_2} →
    {M : Type u_4} →
      [inst : CommSemiring A] →
        [inst_1 : Monoid G] →
          [inst_2 : AddCommMonoid M] →
            [inst_3 : Module (MonoidAlgebra A G) M] →
              Submodule (MonoidAlgebra A G) M ≃o Subrepresentation (Representation.ofModule M)

An order-preserving equivalence between A[G]-submodules of an A[G]-module M and subrepresentations of ρ.

Defined in

Mathlib.RepresentationTheory.Subrepresentation

Cited by

4 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule