proposition: Lemma is_unique_filtered_cocone_morphism {Y : SET} (cc : cocone d Y) (f : SET⟦FilteredColimitSET, Y⟧) (fmor : is_cocone_mor filtered_cocone cc f) : f = filtered_cocone_morphism cc.
proof: Proof. apply funextfun; intro x. apply(surjectionisepitosets (setquotpr filtered_eqrel)). - apply issurjsetquotpr. - apply setproperty. - intro b. exact(eqtohomot (fmor b) b). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.Sets UniMath.MoreFoundations.QuotientSet UniMath.MoreFoundations.Subtypes UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Filtered UniMath.CategoryTheory.Limits.StandardDiagrams UniMath.CategoryTheory.Categories.HSET.Core UniMath.Combinatorics.FiniteSets UniMath.Combinatorics.KFiniteTypes UniMath.Combinatorics.KFiniteSubtypes