A query regarding the hierarchy of monotone Complexity Classes I have recently started studying the monotone complexity classes. There doesn't seem to be a single/clear containment hierarchy or single source regarding the same. Can we create one?

The classes are namely: $mTC^0, mNC^0, mNC, mAL, mcoNL, mL, mNL, mP, mNP, mP/Poly$. (I think that covers most)

The relationships I am aware of:


$mTC^0 \subset mNC^0 \subset mL$
$mL \subset mNL$
$(mP = mAL) \subset mNP$
$mNC \neq mP$


My queries about containment relationship b/w:


$mNC$ vs. $mP$
$mP/Poly$ vs. $mP$


Please feel free to add Open Questions and other known relationships b/w these classes as you see fit.
Raz and McKenzie, Separation of the monotone NC hierarchy, showed that the monotone NC hierarchy is strict, and separated it from monotone P. In all of these separations, the upper bound holds for the uniform class while the lower bound holds even for the non-uniform class (so by monotone P, they really mean monotone P/poly).

Monotone P is easy to separate from monotone P/poly since the latter contains uncomputable functions. For example, the language $\{w : |w| \in K\}$ is in monotone P/poly for any $K \subseteq \mathbb N$, but isn't in monotone P if $K$ is uncomputable.

(By the way, there are several reasonable ways to define monotone P, and I'm not sure they are all equivalent. However, all of them should satisfy what I wrote in the preceding paragraph.)