proposition: Lemma CoAlg_is_precategory {C : category} (F : functor C C) : is_precategory (CoAlg_precategory_data F).
proof: Proof. split. - split. + intros. apply coalgebra_homo_eq. * apply C. * apply id_left. + intros. apply coalgebra_homo_eq. * apply C. * apply id_right. - { split. - intros. apply coalgebra_homo_eq. + apply C. + apply assoc. - intros. apply coalgebra_homo_eq. + apply C. + apply assoc'. } Defined.
imports: UniMath.Foundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Terminal