Lemma contr_cat_eq {F : functor C D} (ff : fully_faithful F) : C = D. Proof. apply subtypePath. - intro; apply isapropiscontr. - apply catiso_to_category_path. use tpair. + exact F. + apply contr_cat_fully_faithful_to_isiso; assumption. Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.Categories.HSET.Core.