proposition: Proposition composition_preserves_hor_comp {C₁ C₂ C₃ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {D₃ : twosided_disp_cat C₃ C₃} {Cm₁ : hor_comp D₁} {Cm₂ : hor_comp D₂} {Cm₃ : hor_comp D₃} {F : C₁ ⟶ C₂} {G : C₂ ⟶ C₃} {FF : twosided_disp_functor F F D₁ D₂} (FFc : preserves_hor_comp Cm₁ Cm₂ FF) {GG : twosided_disp_functor G G D₂ D₃} (GGc : preserves_hor_comp Cm₂ Cm₃ GG) : preserves_hor_comp Cm₁ Cm₃ (comp_twosided_disp_functor FF GG).
proof: Proof. use make_preserves_hor_comp. - exact (composition_preserves_hor_comp_data FFc GGc). - exact (composition_preserves_hor_comp_laws FFc GGc). Defined.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics