Theorems · Definition · group theory

AddCon.congr

{M : Type u_1} →
  {N : Type u_2} →
    [inst : Add M] →
      [inst_1 : Add N] →
        {c : AddCon M} → {d : AddCon N} → (e : M ≃+ N) → c = AddCon.comap ⇑e ⋯ d → c.Quotient ≃+ d.Quotient

An additive equivalence e : α ≃+ β generates an equivalence between quotient spaces, if it is compatible with the relations.

Defined in

Mathlib.GroupTheory.Congruence.Basic

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

AddAdd