Categorical properties of L-fuzzifying convergence spaces

Abstract

In this paper, categorical properties of $L$-fuzzifying convergence spaces are investigated. It is shown that (1) the category $L$-{\bf FYC} of $L$-fuzzifying convergence spaces is a strong topological universe; (2) the category $L$-{\bf FYKC} of $L$-fuzzifying Kent convergence spaces, as a bireflective and bicoreflective full subcategory of $L$-{\bf FYC}, is also a strong topological universe; (3) the category $L$-{\bf FYLC} of $L$-fuzzifying limit spaces, as a bireflective full subcategory of $L$-{\bf FYKC}, is a topological universe.