Section equalizer_of_morphs_from_ids_endomorphs_equalizer_iso.
Context
{d : C}
(f g : (ids_endomorphs_equalizer –≻ d)%morphism)
.
(** Let's show ids_endomorphs_equalizer with V, we construct for any pair of morphisms f, g : V –≻ d, their equalizer (U, e : U –≻ V). *)
Definition equalizer_of_morphs_from_ids_endomorphs_equalizer
:
Equalizer f g
:=
Equalizer_as_Limit
f
g
(LimitOf (Equalizer_Producing_Func f g))
.

(* Specifications: *)
Theorem equalizer_of_morphs_from_ids_endomorphs_equalizer_iso_RI :
((equalizer_morph (equalizer_of_morphs_from_ids_endomorphs_equalizer))
∘
((SSC_Prod_WI _)
∘ (equalizer_morph ids_endomorphs_equalizer)))%morphism
=
id.
Theorem equalizer_of_morphs_from_ids_endomorphs_equalizer_iso_LI :
(((SSC_Prod_WI _) ∘ (equalizer_morph ids_endomorphs_equalizer))
∘
(equalizer_morph (equalizer_of_morphs_from_ids_endomorphs_equalizer))
)%morphism
=
id.