fact: Definition functor_total_category_of_set_functor_on_comp {C₁ C₂ C₃ : setcategory} {F₁ : C₁ ⟶ C₂} {F₂ : C₂ ⟶ C₃} {G₁ : C₁ ⟶ cat_of_setcategory} {G₂ : C₂ ⟶ cat_of_setcategory} {G₃ : C₃ ⟶ cat_of_setcategory} (α : G₁ ⟹ F₁ ∙ G₂) (β : G₂ ⟹ F₂ ∙ G₃) : functor_total_category_of_set_functor F₁ α ∙ functor_total_category_of_set_functor F₂ β ⟹ functor_total_category_of_set_functor (F₁ ∙ F₂) (nat_trans_comp _ _ _ α (pre_whisker F₁ β)).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.GrothendieckConstruction.TotalCategory