∞-Categories are generated by [0] and [1]

Proof. The presheaf category \(\sAn = \Fun (\simp \catop ,\An )\) is generated by the representable presheaves under colimits by Theorem 1.8.9. It follows that \(\Cat _{\infty }\) is generated under colimits by their images under the localization functor \(\ac \colon \sAn \to \Cat _{\infty }\), which are the posets \([n]\). The claim now follows, since the Segal condition shows that each \([n]\) is an iterated pushout of copies of \([1]\) along \([0]\). □