fact: Definition preserves_product : UU := ∏ (D : J → C₁) (c : C₁) (ι : ∏ (j : J), c --> D j), isProduct J C₁ D c ι → isProduct J C₂ (λ j, F (D j)) (F c) (λ j, #F (ι j)).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Adjunctions.Core