Lemma is_cocont_constprod_functor1 : ∏ (C : category) (PC : BinProducts C), Exponentials PC → ∏ x : C, is_cocont (constprod_functor1 PC x). Proof. exact @UniMath.CategoryTheory.Chains.OmegaCocontFunctors.is_cocont_constprod_functor1. Defined.
Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Chains.All. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.SubstitutionSystems.SignatureCategory. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.BindingSigToMonad. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial_alt.