powerset operator, catalg) topology, Fuzzy topology, hypergraph functor, frame, Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.), Categories of topological spaces and continuous mappings, (categorically-algebraic, variety, coreflective subcategory, (generalized) attachment in complete lattice, variety-based topological (space, system), right adjoint functor, Preorders, orders, domains and lattices (viewed as categories), completely prime filter, Theory of fuzzy sets, etc., (localic) algebra, spatialization procedure