  By exploiting the description of topological spaces by either neighborhood
systems or filter convergence, we obtain a neighborhood-like presentation of
categories of lax algebras. A notable advantage of this approach is that it
does not require the introduction of a lax extension of the associated monad
functor. As a byproduct, the different philosophies underlying the construction
of fuzzy topological spaces on one hand, and approach spaces on the other, may
be simply expressed in terms of lax algebras.
