1 Generalizable All Variables.
2 Require Import Preamble.
3 Require Import General.
4 Require Import ch1_3_Categories.
5 Require Import ch1_4_Functors.
6 Require Import ch1_5_Isomorphisms.
8 (*******************************************************************************)
9 (* Chapter 7.8: Equivalent Categories *)
10 (*******************************************************************************)
13 Class EquivalentCategories `(C:Category)`(D:Category){Fobj}{Gobj}(F:Functor C D Fobj)(G:Functor D C Gobj) :=
14 { ec_forward : F >>>> G ≃ functor_id C
15 ; ec_backward : G >>>> F ≃ functor_id D
20 (* Definition 7.25: TFAE: F is an equivalence of categories, F is full faithful and essentially surjective *)