(*******************************************************************************) (* Chapter 7.8: Equivalent Categories *) (*******************************************************************************) Generalizable All Variables. Require Import Notations. Require Import Categories_ch1_3. Require Import Functors_ch1_4. Require Import Isomorphisms_ch1_5. Require Import NaturalIsomorphisms_ch7_5. (* Definition 7.24 *) Class EquivalentCategories `(C:Category)`(D:Category){Fobj}{Gobj}(F:Functor C D Fobj)(G:Functor D C Gobj) := { ec_forward : F >>>> G ≃ functor_id C ; ec_backward : G >>>> F ≃ functor_id D }. (* FIXME *) (* Definition 7.25: TFAE: F is an equivalence of categories, F is full faithful and essentially surjective *)