Definition preserves_binproduct_fiber_functor_comprehension (Γ : C) : preserves_binproduct (fiber_functor (comp_cat_comprehension C) Γ) := right_adjoint_preserves_binproduct _ (adj_equivalence_of_cats_inv _ (fiber_functor_comprehension_adj_equiv Γ)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseEqualizers. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.FullyFaithfulDispFunctor. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat. Require Import UniMath.Bicategories.ComprehensionCat.CompCatNotations. Require Import UniMath.Bicategories.ComprehensionCat.DFLCompCat. Require Import UniMath.Bicategories.ComprehensionCat.DFLCompCatNotations.