Proof.
The full inclusion \(\mathrm{Op}_2 \hookrightarrow \mathrm{Op}\) admits a left adjoint \(h_2 \colon \mathrm{Op}\rightarrow\mathrm{Op}_2\) (constructed in [SY20, Thm. 3.12]). Moreover, it follows from [SY19, Prop. 3.2.6(4)] applied to corollary 7.7.6 that the operad map \(h_2(\mathbb A_2\otimes \mathbb E_1) \rightarrow h_2(\mathbb E_2)\) is an equivalence (i.e. that \(\mathbb A_2 \otimes \mathbb E_1 \rightarrow\mathbb E_2\) is a \(1\)-equivalence in the terminology of [SY19]). By adjunction, it follows that for any \(2\)-operad \(\mathcal O\), the map \(\mathrm{Hom}_{\mathrm{Op}}(\mathbb A_2\otimes \mathbb E_1, \mathcal O) \rightarrow\mathrm{Hom}_{\mathrm{Op}}(\mathbb E_2, \mathcal O)\) is an equivalence. ◻