proposition: Proposition preserves_terminal_fiber_disp_codomain_functor {C₁ C₂ : category} (F : C₁ ⟶ C₂) (x : C₁) : preserves_terminal (fiber_functor (disp_codomain_functor F) x).
proof: Proof. intros y Hy. use isTerminal_codomain_fib ; cbn. use functor_on_is_z_isomorphism. exact (is_z_iso_from_isTerminal_codomain _ Hy). Defined.
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