Proposition weak_equiv_reflects_terminal {C D : category} (F : C ⟶ D) : is_weak_equiv F → ∏ c : C, isTerminal _ (F c) → isTerminal _ c. Proof. intros Fw c Fc_term c'. apply (iscontrweqb' (Fc_term (F c'))). apply ((_ ,, ff_from_weak_equiv _ Fw _ _))%weq. 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.