Theorems · Definition · group theory

MonoidHom.domRestrictHomKerEquiv

{G : Type u} →
  [inst : Group G] →
    (A : Type u_1) →
      [inst_1 : CommGroup A] →
        (H : Subgroup G) → [inst_2 : H.Normal] → ↥(MonoidHom.domRestrictHom H A).ker ≃* (G ⧸ H →* A)

The MulEquiv between the kernel of the restriction map to a normal subgroup H of homomorphisms of type G →* A and the group of homomorphisms G ⧸ H →* A.

Defined in

Mathlib.GroupTheory.QuotientGroup.Basic

Cited by

6 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupCommGroupSubgroup.Normal