English

A Kleisli-based approach to lax algebras

Category Theory 2007-05-23 v2 General Topology

Abstract

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.

Keywords

Cite

@article{arxiv.math/0510281,
  title  = {A Kleisli-based approach to lax algebras},
  author = {Gavin J. Seal},
  journal= {arXiv preprint arXiv:math/0510281},
  year   = {2007}
}

Comments

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)