proposition: Proposition disp_codomain_functor_axioms {C₁ C₂ : category} (F : C₁ ⟶ C₂) : disp_functor_axioms (disp_codomain_functor_data F).
proof: Proof. split. - intros x yf. use eq_cod_mor. rewrite transportb_cod_disp. cbn. rewrite functor_id. apply idpath. - intros x₁ x₂ y₃ yf₁ yf₂ yf₃ f₁ f₂ gp₁ gp₂. use eq_cod_mor. rewrite transportb_cod_disp. cbn. rewrite functor_comp. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations