Corollary weak_equiv_preserves_terminal {C D : category} (F : C ⟶ D) : is_weak_equiv F → preserves_terminal F. Proof. intros Fw ? x_is_t. apply (preserves_terminal_if_preserves_chosen (_,,x_is_t)). - apply weak_equiv_preserves_chosen_terminal. exact Fw. - exact x_is_t. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.WeakEquivalences.Core. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Preservation.