Definition from_iterated_slice_data : functor_data (C/y/xf) (C/x). Proof. use make_functor_data. - exact (λ h, make_cod_fib_ob (dom_mor (cod_mor h))). - simple refine (λ h₁ h₂ p, make_cod_fib_mor _ _). + exact (dom_mor (dom_mor p)). + abstract (cbn ; pose (maponpaths pr1 (mor_eq p)) as q ; cbn in q ; rewrite transportf_cod_disp in q ; exact q). Defined.
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.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Limits.PreservationProperties. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodColimits.