Is the forgetfull functor between the category of n-categories and the category of n-globular sets always monadic?
It's seems so, but, in nLab, they are talking only about "2-globular sets and 2-categories". I wonder if I was missing something...
And how about n-computads for strict n-categories? Are n-categories always monadic over the n-computads?
Thank you in advance
The article Strict $\omega$-categories are monadic over polygraphs Mé16 by F. Métayer answers positively to the (non-strict!) monadicity of the category $n\text{-}\mathbf{Cat}$ of $n$-categories over the category $n\text{-}\mathbf{Pol}$ of $n$-computads (aka $n$-polygraphs).
The strict monadicity of $n$-categories over the category $n\text{-}\mathbf{Glob}$ of $n$-globular sets is easier and references for very general monadicity theorems which apply for presheaves categories, such as $n\text{-}\mathbf{Glob}$ and unlike $n\text{-}\mathbf{Pol}$, can be found in Mé16, as well.