Lemma is_omega_cont_BinProduct_of_functors {C D : category} (F G : functor C D) (PD : BinProducts D) (HF : is_omega_cont F) (HG : is_omega_cont G) : is_omega_cont (BinProduct_of_functors _ _ PD F G). Proof. use (is_omega_cocont_op (F := functor_op (BinProduct_of_functors C D PD F G))). use (is_omega_cocont_BinCoproduct_of_functors _ (functor_op F) (functor_op G) (is_omega_cont_op HF) (is_omega_cont_op HG) ). 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.Limits. 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.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.opp_precat. 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.Colimits. 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. Require Import UniMath.CategoryTheory.Chains.Cochains. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.OppositeCategory.LimitsAsColimits. Require Import UniMath.CategoryTheory.OppositeCategory.OppositeOfFunctorCategory. Require Import UniMath.CategoryTheory.Chains.OmegaCocontFunctors. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses.