Proposition precat_fincard_is_precategory : is_precategory precat_fincard_data. Proof. unfold precat_Delta_precategory_data. unfold is_precategory. split. { split. - intros a b f. unfold "id". simpl in *. reflexivity. - intros a b f. unfold "id". simpl in *. reflexivity. } { split. - reflexivity. - reflexivity. } Qed.
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.