X-Git-Url: http://git.megacz.com/?p=coq-categories.git;a=blobdiff_plain;f=src%2FSectionRetract_ch2_4.v;h=17ab24a34ed8dfe059de239b9b5213dae0896301;hp=3eda753e5fd4ebd20fe8ecfe31063d07a8003870;hb=add4d471e2d188c62bddbdaa21380ee5904bdedc;hpb=ff3003c261295c60d367580b6700396102eb5a9c

diff --git a/src/SectionRetract_ch2_4.v b/src/SectionRetract_ch2_4.v
index 3eda753..17ab24a 100644
--- a/src/SectionRetract_ch2_4.v
+++ b/src/SectionRetract_ch2_4.v
@@ -4,6 +4,7 @@ Require Import Categories_ch1_3.
 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                                      *)
@@ -54,3 +55,13 @@ Instance retract_prod `{C:Category}`{D:Category}{a b:C}{d e:D}(r1:a ⊆ b)(r2:d
 }.
   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.