Definition disp_functor_composite_data {C C' C'' : category} {D} {D'} {D''} {F : functor C C'} {F' : functor C' C''} (FF : disp_functor F D D') (FF' : disp_functor F' D' D'') : disp_functor_data (functor_composite F F') D D''. Proof. use tpair. + intros x xx. exact (FF' _ (FF _ xx)). + intros x y xx yy f ff. exact (♯ FF' (♯ FF ff)). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.