Definition id_preserves_exponentials {C : category} {BC : BinProducts C} (E : Exponentials BC) : preserves_exponentials E E (identity_preserves_binproduct _). Proof. intros x y. use is_z_isomorphism_path. - apply identity. - apply preserves_exponentials_map_id. - apply identity_is_z_iso. Defined.
Require Import UniMath.Foundations.All. 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.Adjunctions.Core. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.CategoryEquality. Require Import UniMath.CategoryTheory.Core.Univalence.