fact: Definition tuple_functor_data {I : UU} {A : category} {B : I → category} (F : ∏ i, A ⟶ (B i)) : functor_data A (product_category B).
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat