ScalingStacks

Example 7.1.5.

It follows from lemma 7.1.3 that for any unital \(\infty\)-operad \(\mathcal O\) and \(\infty\)-operad \(\mathcal P\) the operad \(\mathrm{Alg}_{\mathcal O}(\mathcal P) \simeq \mathrm{Alg}_{\mathcal O\otimes \mathbb E_0}(\mathcal P) \simeq \mathrm{Alg}_{\mathbb E_0}(\mathrm{Alg}_{\mathcal O}(\mathcal P))\) is unital. In particular, since \(\mathbb E_n\) is a unital \(\infty\)-operad for any \(n \geq 0\), it follows that for any \(\infty\)-operad \(\mathcal P\), the \(\infty\)-operads \(\mathrm{Alg}_{\mathbb E_n}(\mathcal P)\) are unital.