[This answer](https://mathoverflow.net/a/55356/148161) states that the category of finitary monads is locally presentable and monadic over the category $\mathrm{Set}^{\mathbb{N}}$. Where can I find proof of this claim?


More generally: I've looked through the literature in nlab ([finitary monad](https://ncatlab.org/nlab/show/finitary+monad), [monad](https://ncatlab.org/nlab/show/monad#References), [Lawvere theory](https://ncatlab.org/nlab/show/Lawvere+theory#references)) and found nothing about this category other than a proof of its equivalence with the category of Lawvere theories (written in several places). I would welcome links to any literature that discusses this category in more detail.



Literature about the category of finitary monads
These claims are proven more generally for the category $\mathrm{Mnd}\_f(\mathscr A)$ of finitary monads on a locally presentable category $\mathscr A$ in Lack's [On the monadicity of finitary monads](https://www.sciencedirect.com/science/article/pii/S0022404999000195). (This is the same Lack as in the linked answer.)


