Did not get an answer from the Stack Exchange.


Let $MonCat$ and $Cat$ denote the 2-categories of monoidal categories with strict monoidal functors and small categories, respectively.


There is a forgetful functor $Forget:MonCat\rightarrow Cat$ Does this preserve (filtered) colimits? I am thinking of 2-colimits in MonCat.



Forgetful Functor $MonCat\rightarrow Cat$ preserves filtered colimits?
Yes. Intuitively, this is because all the operations of a monoidal category are "finitary".


One way to prove this formally is that the 2-monad for monoidal categories can be given a presentation in the category of finitary 2-monads, hence it is finitary (which is equivaent to its forgetful functor preserving filtered colimits). A good reference for presentations of 2-monads is Steve Lack's [A 2-categories companion](https://arxiv.org/abs/math/0702535).


