Require Import Functors_ch1_4.
Require Import Isomorphisms_ch1_5.
Require Import ProductCategories_ch1_6_1.
+Require Import NaturalIsomorphisms_ch7_5.
(******************************************************************************)
(* Chapter 2.4: Sections and Retractions *)
}.
simpl; split; apply retract_pf.
Defined.
+
+Structure RetractionOfCategories `{C:Category} `{D:Category} :=
+{ retraction_section_fobj : C -> D
+; retraction_section : Functor C D retraction_section_fobj
+; retraction_retraction_fobj : D -> C
+; retraction_retraction : Functor D C retraction_retraction_fobj
+; retraction_composes : retraction_section >>>> retraction_retraction ≃ functor_id _
+}.
+Implicit Arguments RetractionOfCategories [ [Ob] [Hom] [Ob0] [Hom0] ].
+Coercion retraction_section : RetractionOfCategories >-> Functor.