proposition: Lemma is_functor_ColimFunctor_data : is_functor ColimFunctor_data.
proof: Proof. split. - intro a; simpl. apply pathsinv0, colim_endo_is_identity; intro u. unfold ColimFunctor_mor. now rewrite colimOfArrowsIn, (functor_id (dob D u)), id_left. - intros a b c fab fbc; simpl; unfold ColimFunctor_mor. apply pathsinv0. eapply pathscomp0; [now apply precompWithColimOfArrows|]. apply pathsinv0, colimArrowUnique; intro u. rewrite colimOfArrowsIn. rewrite (functor_comp (dob D u)). now apply pathsinv0, assoc. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core