2005/10/13 by Gavin J. Seal, Seal, Gavin J.
Computer Science · Decision Sciences · Mathematics · #18C20 (Primary) 18B30 #54A05 (Secondary) #Advanced Algebra and Logic #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #math.CT #math.GN #msc:18B30 #msc:18C20 #msc:54A05
paper · pdf · doi:10.48550/arxiv.math/0510281
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)
openalex publication_date 2005/10/13 · arxiv created 2006/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.