Definition 14.2.5. Given a symmetric monoidal \(\infty \)-category \(C\), we denote its cocartesian unstraightening by \[ C^{\otimes } \quad := \quad \Un ^{\cc }(C\colon \Span (\Fin ) \to \Cat _{\infty }). \] By the previous lemma, the resulting cocartesian fibration \(p_C\colon C^{\otimes } \to \Span (\Fin )\) defines an \(\infty \)-operad, which we will denote by \(\Mm _C := (C^{\otimes },p_C)\) and refer to as the multimorphism operad associated to \(C\). By functoriality of unstraightening, this defines a (non-full) inclusion \[ \Mm \colon \Cat _{\infty }^{\otimes } \hookrightarrow \Op _{\infty }. \] Morphisms in its essential image are studied in the next section.
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