Consider a $2$-monad $ T: \mathfrak{X}\to \mathfrak{X} $ and consider its 2-category of pseudoalgebras $PsAlg$. There is a forgetful functor $ U: PsAlg\to \mathfrak{X} $.
Does this forgetful functor reflect equivalences?
I couldn't find any mention of this fact in the literature that I've been reading. But this can be a trivial question.
Thank you in advance.