Lemma 21.5.6. Let \(C\) be an \(\infty \)-category that admits an initial (resp. terminal) object \(x\colon * \to C\). Then \(C\) is weakly contractible: \(\geom {C} \simeq *\).
Proof. By Remark 21.2.3 we have an adjunction \(x\colon * \rightleftarrows C \noloc p_C\), which by Lemma 21.1.7 induces an equivalence \(* \simeq \geom {*} \simeq \geom {C}\). □
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