Definition FinOrdStrict : strict_monoidal_cat. Proof. use tpair. { exact AugmentedSimplexCategory. } cbv beta. intros eq_λ eq_ρ eq_α. use tpair. { exact (tensor_Δ_left_unitor_is_id eq_λ). } split. { exact (tensor_Δ_right_unitor_is_id eq_ρ). } exact (tensor_ord_is_strict_associator_id eq_α). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.CategoryTheory.SimplicialSets.