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