∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] [inst_1 : DecidableEq J]
  (F : CategoryTheory.Functor J AddCommGrpCat) [inst_2 : Small.{w, max u w} (AddCommGrpCat.Colimits.Quot F)],
  AddCommGrpCat.Colimits.Quot.desc F (AddCommGrpCat.Colimits.colimitCocone F) = Shrink.addEquiv.symm.toAddMonoidHom