proposition: Lemma weak_equiv_reflects_terminal {C D : category} (F : C ⟶ D) : is_weak_equiv F → ∏ c : C, isTerminal _ (F c) → isTerminal _ c.
proof: Proof. intros Fw c Fc_term c'. apply (iscontrweqb' (Fc_term (F c'))). apply ((_ ,, ff_from_weak_equiv _ Fw _ _))%weq. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.catiso UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecompEquivalence