Example 14.1.14. The \(\infty \)-operad \(\Ee _0\) of pointed objects is given by \[ \Ee _0^{\otimes } := \Span _{\all ,\inj }(\Fin ) \qquadtext { and } p_{\Ee _0} = \incl \colon \Span _{\all ,\inj }(\Fin ) \hookrightarrow \Span (\Fin ). \] The active maps in \(\Ee _0\) are the injections \(I \hookrightarrow J\) of finite sets. The finite-product conditions in the definition of an \(\infty \)-operad follow from part (1) of Lemma 13.3.8; the fibers of \(p_{\Ee _0}\) are contractible, and the backwards spans remain cocartesian under the inclusion into \(\Span (\Fin )\).
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