Definition codomain_fib_binproducts (x : C) : BinProducts (C/x). Proof. intros fy₁ fy₂. pose (P := HC _ _ _ (cod_mor fy₁) (cod_mor fy₂)). use make_BinProduct. - refine (PullbackObject P ,, _). exact (PullbackPr1 P · cod_mor fy₁). - refine (PullbackPr1 P ,, _). abstract (cbn ; rewrite id_right ; apply idpath). - refine (PullbackPr2 P ,, _). abstract (cbn ; rewrite PullbackSqrCommutes ; rewrite id_right ; apply idpath). - use isPullback_to_isBinProduct_cod_fib. apply P. 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.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.PullbackConstructions. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseEqualizers. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint. Section FromEqCodFib. End FromEqCodFib. Section FromUMP. End FromUMP.