Lemma covyoneda_map_2_1 (C : category) (c : C) (F : functor C HSET) (x : pr1 (F c)) : covyoneda_map_1 _ _ _ (covyoneda_map_2 _ _ _ x) = x. Proof. simpl. rewrite (functor_id F). apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering.