Let's assume infinitely many Grothendieck universes exist. Let's call $\kappa$-Cat the bicategory of $\kappa$-small categories with anafunctors and anatural transformations. Now for any $\lambda$ and a $\lambda$-small 1-category $C$; we have a bicategory of monads $Mnd(C)$. Is there for all $\kappa$ a pair $\lambda$ and a $\lambda$-small 1-category $C$, such that $\kappa$-Cat $=$ $Mnd(C)$?