functors, categories, fuzzy topological spaces, fuzzy closude spaces

In the present work we consider several categories with a weaker structurethan that of an L-valued topology, namely the categories of Cech L-fuzzy interiorspaces, Cech L-fuzzy closure spaces, categories of L-fuzzy pretopological spacesand L-fuzzy co-pretopological spaces, the category of reflexive L-fuzzy relationsand, finally, the category of spaces with L-fuzzy partitions. We connect all thesecategories and some of their subcategories using commutative diagrams of functors.