Theorems · Definition · group theory

Rep.indResHomEquiv

{k : Type u} →
  {G : Type v} →
    {H : Type v'} →
      [inst : CommRing k] →
        [inst_1 : Group G] →
          [inst_2 : Group H] →
            (φ : G →* H) →
              (A : Rep.{max w v' u, u, v} k G) →
                (B : Rep.{max w v' u, u, v'} k H) → (Rep.ind φ A ⟶ B) ≃ₗ[k] A ⟶ Rep.res φ B

Given a group homomorphism φ : G →* H, an H-representation B, and a G-representation A, there is a k-linear equivalence between the H-representation morphisms ind φ A ⟶ B and the G-representation morphisms A ⟶ B.

Defined in

Mathlib.RepresentationTheory.Induced

Cited by

4 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupGroup