Theorems · Definition · group theory

Con.mapOfSurjective

{M : Type u_1} →
  {N : Type u_2} →
    {F : Type u_4} →
      [inst : Mul M] →
        [inst_1 : Mul N] →
          [inst_2 : FunLike F M N] →
            [inst_3 : MulHomClass F M N] → {c : Con M} → (f : F) → Con.ker f ≤ c → Function.Surjective ⇑f → Con N

Given a surjective multiplicative-preserving function f whose kernel is contained in a congruence relation c, the congruence relation on f's codomain defined by 'x ≈ y iff the elements of f⁻¹(x) are related to the elements of f⁻¹(y) by c.'

Defined in

Mathlib.GroupTheory.Congruence.Hom

Cited by

1 results in Mathlib

Foundations

Depth 11 from the axioms · uses no axioms

Assumes

MulMulFunLikeMulHomClass