Definition make_enrichment_over_poset_data : enrichment_data C poset_monoidal_cat. Proof. simple refine (_ ,, _ ,, _ ,, _ ,, _). - exact (λ x y, _ ,, PEC x y). - refine (λ x, (λ _, identity _) ,, _). abstract (cbn ; intros t₁ t₂ p ; apply refl_PartialOrder). - simple refine (λ x y z, _ ,, _) ; cbn in *. + exact (λ fg, pr2 fg · pr1 fg). + abstract (intros fg₁ fg₂ p ; cbn in * ; exact (trans_PartialOrder _ (poset_enrichment_comp_l PEC _ (pr2 p)) (poset_enrichment_comp_r PEC _ (pr1 p)))). - refine (λ x y f, (λ _, f) ,, _). abstract (intros t₁ t₂ p ; cbn in * ; apply refl_PartialOrder). - exact (λ x y f, pr1 f tt). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.CategoryOfPosets. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.PosetsMonoidal. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Section FromPosetEnrichment. End FromPosetEnrichment.