Proposition 17.3.13. The multimorphism operad functor \(\Mm \colon \Cat _{\infty }^{\otimes } \to \Op _{\infty }\) admits a left adjoint \[ \Env \colon \Op _{\infty } \to \Cat _{\infty }^{\otimes }. \]
Proof. This is a special case of the previous proposition. For \(\Ff = (\Fin ,\Fin ,\Fin )\), Proposition 14.1.9 identifies the objects of \(\Op _{\Ff }\) with the \(\infty \)-operads from Definition 14.1.1, while Corollary 14.1.11 identifies the two notions of morphism. □
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