Definition weq_filtered (J : category) : is_filtered J ≃ is_filtered_alt J. Proof. use weqimplimpl. - exact filtered_to_filtered_alt. - exact filtered_alt_to_filtered. - exact isaprop_is_filtered. - exact isaprop_is_filtered_alt. Defined.
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.