fact: Definition pr_functor (I : UU) (C : I -> category) (i : I) : (product_category C) ⟶ (C i).
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat