Theorems · Definition · group theory

QuotientGroup.map

{G : Type u_1} →
  {H : Type u_2} →
    [inst : Group G] →
      [inst_1 : Group H] →
        (N : Subgroup G) →
          [nN : N.Normal] →
            (M : Subgroup H) → [inst_2 : M.Normal] → (f : G →* H) → N ≤ Subgroup.comap f M → G ⧸ N →* H ⧸ M

A group homomorphism f : G →* H induces a map G/N →* H/M if N ⊆ f⁻¹(M).

Defined in

Mathlib.GroupTheory.QuotientGroup.Defs

Cited by

14 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupSubgroup.NormalSubgroup.Normal