Definition terminal_mor_lift {x y : C} (f : x --> y) : terminal_obj_in_fib T x -->[ f ] terminal_obj_in_fib T y := transportf _ (id_left f) (TerminalArrow (lift_terminal_in_fib T f) _ ;; HD y x f (terminal_obj_in_fib T y))%mor_disp.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Preservation. Section RightAdjointFromTerminal. End RightAdjointFromTerminal.