Definition filtered_cocone_morphism {Y : SET} (cc : cocone d Y) : SET⟦FilteredColimitSET, Y⟧. Proof. use setquotuniv. - exact(from_cobase cc). - exact(iscomprelfun_from_cobase cc). 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.