Definition preserves_initial_cod_pb_iterated (H : preserves_initial (cod_pb PB (dom_mor h))) : preserves_initial (cod_pb PB₁ h) := preserves_initial_equivalence_b _ _ (from_iterated_slice_adj_equivalence_of_cats _) (from_iterated_slice_adj_equivalence_of_cats _) (cod_pb PB₁ h) (cod_pb PB (dom_mor h)) iterated_slice_pb_nat_z_iso H.
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.