Lemma 4.3.12 (Universal property of finite pointed animae). Let \(\An _*^{\fin }\) be the small full subcategory of \(\An _*\) generated under finite colimits by \(S^0\). For every pointed \(\infty \)-category \(D\) with finite limits, evaluation at \(S^0\) induces an equivalence \[ \ev _{S^0}\colon \Fun ^{\lex }((\An _*^{\fin })\catop ,D) \iso D. \]
Proof. This is the opposite of the universal property of the free finite cocompletion of the point, which is a special case of Proposition 22.1.2. □
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