Theorems · Definition · group theory

Rep.mkIso

{k : Type u} →
  {G : Type v} →
    [inst : Semiring k] →
      [inst_1 : Monoid G] →
        {X Y : Type w} →
          [inst_2 : AddCommGroup X] →
            [inst_3 : AddCommGroup Y] →
              [inst_4 : Module k X] →
                [inst_5 : Module k Y] →
                  {ρ : Representation k G X} → {σ : Representation k G Y} → ρ.Equiv σ → (Rep.of ρ ≅ Rep.of σ)

An equiv between the underlying representations induce isomorphism between objects in Rep k G.

Defined in

Mathlib.RepresentationTheory.Rep.Basic

Cited by

7 results in Mathlib

Foundations

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

Assumes

SemiringMonoidAddCommGroupAddCommGroupModuleModule