Theorems · Definition · group theory

QuotientAddGroup.map

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

An AddGroup homomorphism f : G →+ H induces a map G/N →+ H/M if N ⊆ f⁻¹(M).

Defined in

Mathlib.GroupTheory.QuotientGroup.Defs

Cited by

10 results in Mathlib

Foundations

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

Assumes

AddGroupAddGroupAddSubgroup.NormalAddSubgroup.Normal