Structured lattices and topological categories of L-sets
Goguen's category of V-sets whose objects are functions with values in a pre-ordered set and morphisms are suitable maps is shown to be a topological construct if and only if the pre-ordered set is a complete lattice; in particular the category Set(L) of L-sets, also considered by Goguen, is topological over Set. The special case when the considered pre-ordered set is L with the "mapping to" relation arising from a structure Phi = (phi(a))(a is an element of L), where every phi(a) : L -> [perpendicular to, a] preserves arbitrary infs, already considered by the authors on any complete lattice L, is investigated in detail. (C) 2009 Elsevier B.V. All fights reserved.
topological category fuzzy set powerset operator ground category adjoint functors