Proposition disp_mono_codomain_fiber_functor_essentially_surjective (HF' : essentially_surjective F) (HF'' : fully_faithful F) (x : C₁) : essentially_surjective (fiber_functor disp_mono_codomain_functor x). Proof. exact (fiber_functor_essentially_surjective _ (disp_mono_codomain_functor_ess_surj HF' HF'') x). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.MonoCodomain. Require Import UniMath.CategoryTheory.DisplayedCats.MonoCodomain.FiberMonoCod.