Theorems · Theorem · group theory

Representation.IndV.hom_ext

∀ {k : Type u_1} {G : Type u_2} {H : Type u_3} [inst : CommRing k] [inst_1 : Group G] [inst_2 : Group H] (φ : G →* H)
  {A : Type u_4} {B : Type u_5} [inst_3 : AddCommGroup A] [inst_4 : Module k A] (ρ : Representation k G A)
  [inst_5 : AddCommGroup B] [inst_6 : Module k B] {f g : Representation.IndV φ ρ →ₗ[k] B},
  (∀ (h : H), f ∘ₗ Representation.IndV.mk φ ρ h = g ∘ₗ Representation.IndV.mk φ ρ h) → f = g

Defined in

Mathlib.RepresentationTheory.Induced

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupGroupAddCommGroupModuleAddCommGroupModule