Proposition cat_property_laws_conj (P₁ P₂ : cat_property) : cat_property_laws (cat_property_data_conj P₁ P₂). Proof. refine (_ ,, _ ,, _ ,, _). - intros C. apply isapropdirprod. + apply isaprop_cat_property_ob. + apply isaprop_cat_property_ob. - intros C₁ C₂ H₁ H₂ F. apply isapropdirprod. + apply isaprop_cat_property_functor. + apply isaprop_cat_property_functor. - intros C H. split. + apply cat_property_id_functor. + apply cat_property_id_functor. - intros C₁ C₂ C₃ H₁ H₂ H₃ F G HF HG. split. + exact (cat_property_comp_functor P₁ (pr1 HF) (pr1 HG)). + exact (cat_property_comp_functor P₂ (pr2 HF) (pr2 HG)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpi. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpiFacts. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory. Require Import UniMath.CategoryTheory.RegularAndExact.ExactCategory. Require Import UniMath.CategoryTheory.Arithmetic.ParameterizedNNO. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseSubobjectClassifier. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodFunctor. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodColimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.ColimitProperties. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodRegular. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodSubobjectClassifier. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodNNO. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.StrictInitial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.DisjointBinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifierIso. Require Import UniMath.CategoryTheory.SubobjectClassifier.PreservesSubobjectClassifier. Require Import UniMath.Bicategories.Core.Examples.StructuredCategories. Require Import UniMath.Bicategories.ComprehensionCat.LocalProperty.LocalProperties.