Definition strict_initial_cod_fib (I : strict_initial_object C) : strict_initial_object (C/x). Proof. use make_strict_initial. - exact (initial_cod_fib x I). - apply is_strict_initial_cod_fib. exact (is_strict_initial_strict_initial I). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.StrictInitial. Require Import UniMath.CategoryTheory.Limits.DisjointBinCoproducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. 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.CodMorphisms. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodColimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.IteratedSlice. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodFunctor.