Definition kfinite_subsets_cocone : cocone d X. Proof. use make_cocone. - exact(λ (A : kfinite_subtype X), pr1). - abstract(red; intros; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.QuotientSet. Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Filtered. Require Import UniMath.CategoryTheory.Limits.StandardDiagrams. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.Combinatorics.KFiniteTypes. Require Import UniMath.Combinatorics.KFiniteSubtypes.