2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103657By 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.15 pages. Revised version of the paper: some notation/wording modifications, improvement of Prop 3.3 i), presentation of the category of Kleisli (T,V)-algebras as a tower extension of Kl(T)Category TheoryGeneral Topology18C20 (Primary) 18B30, 54A05 (Secondary)text