Lemma diagonalMap_isMonic : isMonic (diagonalMap'). Proof. use make_isMonic. intros x g h p. assert (p' := (maponpaths (λ f, compose f (BinProductPr1 C (P B B))) p)). unfold diagonalMap' in p'. rewrite !assoc', BinProductPr1Commutes , !id_right in p'. exact p'. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.Combinatorics.StandardFiniteSets. Section BinProductFromIso. End BinProductFromIso. Section BinProductsFromProducts. End BinProductsFromProducts. Section ProductsFromBinProducts. End ProductsFromBinProducts.