An ordinary (∞,1)-operad$\mathcal{O}$ is equivalently incarnated as its (∞,1)-category of operators$\mathcal{O}^\otimes \to FinSet_*$, which in particular has the property that $\mathcal{O}^{\otimes}_{\langle 0\rangle} \simeq *$.

A generalized $(\infty,1)$-operad is like an (∞,1)-category of operators only that this condition is dropped and