The categorical topology approach to fuzzy topology and fuzzy convergence

Abstract

Abstract It is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology. We first look at interesting subcategories of FTS and determine whether they are bireflective and/or coreflective. We also describe the set of all subcategories of FTS which are at the same time bireflective and coreflective. Due to the fact that TOP is one of these subcategories of FTS, FTS itself can be neither Cartesian closed nor extensional. We therefore, secondly, construct a supercategory of FTS which is a topological quasitopos. The construction of this quasitopos is based on the theory of convergence in FTS.