ScalingStacks

The \(\infty\)-category \(\mathrm{Op}\) of \(\infty\)-operads itself carries a symmetric monoidal structure, called the Boardman-Vogt tensor product uniquely characterized⁵⁷ by giving rise to an equivalence of \(\infty\)-operads for all \(\infty\)-operads \(\mathcal O, \mathcal O'\) and \(\mathcal P\): \[ \mathrm{Alg}_{\mathcal O}(\mathrm{Alg}_{\mathcal O'}(\mathcal P)) \simeq \mathrm{Alg}_{\mathcal O\otimes \mathcal O'}(\mathcal P).\] Equivalently, the Boardman-Vogt tensor product has \(\mathrm{Alg}_{-}(-)\) as its internal hom.