proposition: Lemma tuple_functor_axioms {I : UU} {A : category} {B : I → category} (F : ∏ i, A ⟶ (B i)) : is_functor (tuple_functor_data F).
proof: Proof. split. - intros a. apply funextsec; intro i. apply functor_id. - intros ? ? ? ? ?. apply funextsec; intro i. apply functor_comp. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat