Lemma is_cocont_delta_functor : is_cocont (delta_functor I C). Proof. apply (left_adjoint_cocont _ _ _ (is_left_adjoint_delta_functor _ PC)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Slice. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. 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.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Adjunctions.Examples. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.RightKanExtension. Require Import UniMath.CategoryTheory.slicecat. Require Import UniMath.CategoryTheory.Chains.Chains.