Definition comp_preserves_fiberwise_subobject_classifier {C₁ C₂ C₃ : category} {F : C₁ ⟶ C₂} {G : C₂ ⟶ C₃} {D₁ : disp_cat C₁} {D₂ : disp_cat C₂} {D₃ : disp_cat C₃} {HD₁ : cleaving D₁} {HD₂ : cleaving D₂} {HD₃ : cleaving D₃} {TD₁ : fiberwise_terminal HD₁} {TD₂ : fiberwise_terminal HD₂} {TD₃ : fiberwise_terminal HD₃} {FF : disp_functor F D₁ D₂} {HFF₁ : preserves_fiberwise_terminal FF} (HFF₂ : preserves_fiberwise_subobject_classifier TD₁ TD₂ FF HFF₁) {GG : disp_functor G D₂ D₃} {HGG₁ : preserves_fiberwise_terminal GG} (HGG₂ : preserves_fiberwise_subobject_classifier TD₂ TD₃ GG HGG₁) : preserves_fiberwise_subobject_classifier TD₁ TD₃ (disp_functor_composite FF GG) (comp_preserves_fiberwise_terminal HFF₁ HGG₁).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifierIso. Require Import UniMath.CategoryTheory.SubobjectClassifier.PreservesSubobjectClassifier.