Pointed objects

Example 18.1.7 (Pointed objects). Let \(C\) satisfy the hypotheses of Lemma 16.3.4, and equip \(C_*\) with its smash product monoidal structure. Its zero object is both operadic terminal and operadic initial, so \(\Mm _{C_*}\) is a pointed \(\infty \)-operad. Indeed, operadic terminality is automatic by Example 18.1.3, while operadic initiality says precisely that tensoring with the zero object gives the zero object.