Stratified categorical fixed-basis fuzzy topological spaces and their duality
For an abstract category C, a class M M of C-monomorphisms and a fixed C-object L, we introduce stratified C-M M -L-spaces to be categorical counterparts of stratified fixed-basis fuzzy topological spaces in C, and consider their category SC-M M -L-Top. As two main results of this paper, it is shown that SC-M M -L-Top is dually adjoint to the comma category L?C L ? C , and this adjunction can be restricted to a dual equivalence between the full category of L?C L ? C with comma-spatial objects and the full category of SC-M 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.
fuzzy topology topology comma category category theory categorical topology adjoint situation lattice-valued topology stratified fuzzy topology