Theorems · Theorem · group theory

Representation.Coinvariants.le_comap_ker

∀ {k : Type u_6} {G : Type u_7} {V : Type u_8} [inst : CommRing k] [inst_1 : Group G] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V) (S : Subgroup G) [S.Normal] (g : G),
  Representation.Coinvariants.ker (MonoidHom.comp ρ S.subtype) ≤
    Submodule.comap (ρ g) (Representation.Coinvariants.ker (MonoidHom.comp ρ S.subtype))

Defined in

Mathlib.RepresentationTheory.Coinvariants

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupAddCommGroupModuleSubgroup.Normal