proposition: Proposition disp_codomain_fiber_functor_mor {C₁ C₂ : category} (F : C₁ ⟶ C₂) (x : C₁) {f g : C₁/x} (h : f --> g) : dom_mor (#(fiber_functor (disp_codomain_functor F) x) h) = #F(dom_mor h).
proof: Proof. cbn ; unfold dom_mor. rewrite transportf_cod_disp. cbn. 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