Proposition is_z_iso_from_isTerminal_codomain {x : C} (yf : C/x) (H : isTerminal (C/x) yf) : is_z_isomorphism (pr2 yf). Proof. pose (T := (_ ,, H) : Terminal _). pose (φ := TerminalArrow T (cod_fib_id x)). use make_is_z_isomorphism. - exact (dom_mor φ). - split. + abstract (use (maponpaths dom_mor (TerminalArrowEq (T := T) (_ · _ ,, _) (identity _))) ; cbn ; rewrite !assoc' ; apply maponpaths ; exact (mor_eq φ)). + abstract (exact (mor_eq φ)). Defined.
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.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.PullbackConstructions. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseEqualizers. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint. Section FromEqCodFib. End FromEqCodFib. Section FromUMP. End FromUMP.