Definition slice_constprod_functor1_mor {C : category} (PB : Pullbacks C) {x : C} (BP := codomain_fib_binproducts PB x) (yf : C/x) {zg₁ zg₂ : C/x} (hp : zg₁ --> zg₂) : cod_dom (constprod_functor1 BP yf zg₁) --> cod_dom (constprod_functor1 BP yf zg₂). Proof. use PullbackArrow. - apply PullbackPr1. - exact (PullbackPr2 _ · dom_mor hp). - abstract (cbn ; refine (PullbackSqrCommutes _ @ _) ; rewrite !assoc' ; rewrite (mor_eq hp) ; apply idpath). 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.Adjunctions.Examples. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodDomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodColimits. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodFunctor. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.whiskering. 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.StrictInitial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.DisjointBinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation.