proposition: Lemma discrete_functor {C D : discrete_category} (f : ob C → ob D) : functor C D.
proof: Proof. use make_functor. - use make_functor_data. + apply f. + intros a b atob. pose (aeqb := @univalent_groupoid_arrow_weq_path C _ _ atob). exact (transportf (λ z, _ ⟦ f a, z ⟧) (maponpaths f aeqb) (identity _)). - split. + intro; apply discrete_category_hom_prop. + intros ? ? ? ? ?; apply discrete_category_hom_prop. Defined.
imports: UniMath.Foundations.PartA UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat