Lemma iso_exp_precomp_prod_functor : @z_iso [PreShv C, PreShv C] precomp_prod_functor (exp (Yon c)). Proof. use z_iso_inv_from_z_iso. use (z_iso_comp first_iso_on_functors). use (z_iso_comp second_iso_on_functors). use (z_iso_comp third_iso_on_functors). use fourth_iso_on_functors. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.RightKanExtension. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.yoneda. Require Import UniMath.CategoryTheory.YonedaBinproducts. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Presheaf.