Structured lattices and topological categories of L-sets

5 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, 7 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 = ( a)a∈L , where every a : L → [⊥, a] preserves arbitrary infs, already considered by the 9 authors on any complete lattice L, is investigated in detail. © 2009 Published by Elsevier B.V. 11