On closed lattices
A. Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the definition of normal functor. We investigate as well some topological properties of such extension.
The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of -semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At...