Definition bij_group_quo_ker_coKer :
  Hom (group_quo G (Ker f) (kernel_normal (G:=G) (G':=G') (f:=f)):GROUP)
    (coKer f).

Theorem factor_group_hom : Equal f (comp_hom inj_coKer_group (comp_hom bij_group_quo_ker_coKer surj_group_quo_ker)).