Lemma isaprop_is_filtered_alt {J : category} : isaprop (is_filtered_alt J). Proof. apply isapropdirprod; [apply propproperty |apply isapropdirprod; repeat (apply impred_isaprop; intro; try apply propproperty)]. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.covyoneda. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.CategoryTheory.Limits.StandardDiagrams.