Theorems · Definition · group theory

AddGroupExtension.Equiv.ofAddMonoidHom

{N : Type u_1} →
  {G : Type u_2} →
    [inst : AddGroup N] →
      [inst_1 : AddGroup G] →
        {E : Type u_3} →
          [inst_2 : AddGroup E] →
            {S : AddGroupExtension N E G} →
              {E' : Type u_4} →
                [inst_3 : AddGroup E'] →
                  {S' : AddGroupExtension N E' G} →
                    (f : E →+ E') → f.comp S.inl = S'.inl → S'.rightHom.comp f = S.rightHom → S.Equiv S'

An equivalence of additive group extensions from a homomorphism making a commuting diagram. Such a homomorphism is necessarily an isomorphism.

Defined in

Mathlib.GroupTheory.GroupExtension.Basic

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddGroupAddGroupAddGroup