Definition initial_category_iso_comma (I₁ : Initial C₁) (I₂ : Initial C₂) : Initial (iso_comma F G). Proof. simple refine (_ ,, _). - refine ((pr1 I₁ ,, pr1 I₂) ,, _) ; cbn. exact (ziso_Initials (make_Initial _ (HF _ (pr2 I₁))) (make_Initial _ (HG _ (pr2 I₂)))). - apply isInitial_iso_comma. + exact (pr2 I₁). + exact (pr2 I₂). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation.