proposition: Proposition all_functors_democratic {C₁ C₂ : full_comp_cat} (D₁ : is_democratic C₁) (D₂ : is_democratic C₂) (F : full_comp_cat_functor C₁ C₂) : is_democratic_functor D₁ D₂ F.
proof: Proof. simple refine (_ ,, _). - exact (all_functor_democratic_data D₁ D₂ F). - exact (all_functor_democratic_laws D₁ D₂ F). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.FullyFaithfulDispFunctor UniMath.CategoryTheory.Limits.Terminal UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.ComprehensionCat.BicatOfCompCat UniMath.Bicategories.ComprehensionCat.CompCatNotations