Definition disp_functor_composite {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 (functor_composite F F') D D''. Proof. use tpair. - apply (disp_functor_composite_data FF FF'). - apply disp_functor_composite_axioms. 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.