In the "ordinary" operad category, it is known that there is a colored operad $Op$ with set of colors $\mathbb{N}$ corresponding to "degrees" of vertices and with operations indexed by trees, such that algebras over $Op$ in $\mathrm{Set}$ (or more generally any symmetric monoidal category) correspond to monochromatic operads.


Is it known that $\infty$-algebras over $Op$ are equivalent to monochromatic $\infty$-operads?



Monochromatic infinity operads as algebras over the "operad operad"
Yes, combine Corollary 9.4.1 and Theorem 7.11 of [arXiv:1410.5675](https://arxiv.org/abs/1410.5675), for example.


This topic is also examined more explicitly
in the work of Chu and Haugseng, [arXiv:1707.08049](https://arxiv.org/abs/1707.08049).


Corollary 5.1.13 shows that enriched ∞-operads are equivalent
to ∞-algebras over the operad of colored operads.


Theorem 5.2.10 proves (using [arXiv:1410.5675](https://arxiv.org/abs/1410.5675)) that the underlying ∞-category
of the relative category of ordinary enriched colored operads
is equivalent to the ∞-category of enriched colored ∞-operads.


