Definition self_enrichment_binary_products (PV : BinProducts V) : enrichment_binary_prod (self_enrichment V). Proof. intros v₁ v₂. pose (w := PV v₁ v₂ : V). pose (π₁ := BinProductPr1 _ (PV v₁ v₂) : w --> v₁). pose (π₂ := BinProductPr2 _ (PV v₁ v₂) : w --> v₂). pose (H := pr2 (PV v₁ v₂) : isBinProduct V v₁ v₂ w π₁ π₂). simple refine (_ ,, _). - exact (self_enrichment_binary_products_cone π₁ π₂). - use make_is_binary_prod_enriched. + exact (λ _ _ f g, self_enrichment_pair π₁ π₂ H f g). + exact (λ _ _ f g, self_enrichment_pair_pr1 π₁ π₂ H f g). + exact (λ _ _ f g, self_enrichment_pair_pr2 π₁ π₂ H f g). + exact (λ _ _ f g, self_enrichment_pair_eq π₁ π₂ H f g). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedTerminal. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedBinaryProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedProducts. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedEqualizers. Require Import UniMath.CategoryTheory.EnrichedCats.Limits.EnrichedPowers. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Import MonoidalNotations.