Fundamental duality of abstract categories and its applications

Demirci M.

FUZZY SETS AND SYSTEMS, cilt.256, ss.73-94, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 256
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.fss.2013.08.015
  • Dergi Adı: FUZZY SETS AND SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.73-94
  • Anahtar Kelimeler: Category theory, Duality, Adjoint situation, Stone duality, Categorical topology, Many-valued topology, Fuzzy topology, SEPARATION AXIOMS, REPRESENTATION, FOUNDATIONS, COMPACTNESS, OBJECTS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Given an abstract category C, C-M-L-spaces that are categorical generalization of fixed-basis fuzzy topological spaces in C and their category C-M-L-Top are introduced. It is pointed out, as one of the main contributions of this paper, that C is dually adjoint to C-M-L-Top. By defining L-spatiality in C and L-sobriety in C-M-L-Top, this adjunction induces a dual equivalence between the full subcategory of C of all L-spatial objects and the full subcategory of C-M-L-Top of all L-sober objects. The present adjunction and duality are fruitful categorical extensions of the classical Top-Loc adjunction and SobTop-SpatLoc duality to abstract categories with a great deal of applications. In particular, their applications to Q-categories, quasivarieties and augmented posets are given. (C) 2013 Elsevier B.V. All rights reserved.