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