Functors Among Categories of L-fuzzy Partitions, L-fuzzy Pretopological Spaces and L-fuzzy Closure Spaces

Abstract

In the present work we consider several categories with a weaker structure than that of an L-valued topology, namely the categories of Čech L-fuzzy interior spaces, Čech L-fuzzy closure spaces, categories of L-fuzzy pretopological spaces and L-fuzzy co-pretopological spaces, the category of reflexive L-fuzzy relations and, finally, the category of spaces with L-fuzzy partitions. We connect all these categories and some of their subcategories using commutative diagrams of functors.