proposition: Proposition comp_functor_laws : is_functor comp_functor_data.
proof: Proof. split. - intro g. use eq_mor_cod_fib ; cbn. apply idpath. - intros g₁ g₂ g₃ h₁ h₂. use eq_mor_cod_fib. cbn -[fiber_category]. rewrite !comp_in_cod_fib. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod UniMath.CategoryTheory.DisplayedCats.DependentSums