Stratified categorical fixed-basis fuzzy topological spaces and their duality

DEMİRCİ M.

FUZZY SETS AND SYSTEMS, vol.267, pp.1-17, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 267
  • Publication Date: 2015
  • Doi Number: 10.1016/j.fss.2014.08.005
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-17
  • Keywords: Category theory, Topology, Categorical topology, Adjoint situation, Comma category, Lattice-valued topology, Fuzzy topology, Stratified fuzzy topology, VALUED EQUIVALENCE-RELATIONS, VAGUE LATTICES, FOUNDATIONS, SETS
  • Akdeniz University Affiliated: Yes

Abstract

For an abstract category C, a class M of C-monomorphisms and a fixed C-object L, we introduce stratified C-M-L-spaces to be categorical counterparts of stratified fixed-basis fuzzy topological spaces in C, and consider their category SC-M-L-Top. As two main results of this paper, it is shown that SC-M-L-Top is dually adjoint to the comma category L down arrow C, and this adjunction can be restricted to a dual equivalence between the full category of L down arrow C with comma-spatial objects and the full category of SC-M-L-Top with comma-sober objects. The present paper also describes applications and relationships of these results to stratified fixed-basis fuzzy topological spaces. In this respect, a considerable part of this paper is devoted to stratified L-quasi-topological spaces and their duality. (C) 2014 Elsevier B.V. All rights reserved.