Structured lattices and topological categories of L-sets

  • Authors:

  • A. Frascella;C. Guido

  • Affiliations:

  • Department of Mathematics “E. De Giorgi”, University of Salento, P.O. Box 193, 73100 Lecce, Italy;Department of Mathematics “E. De Giorgi”, University of Salento, P.O. Box 193, 73100 Lecce, Italy

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

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 @F=(@f"a)"a"@?"L, where every @f"a:L-[@?,a] preserves arbitrary infs, already considered by the authors on any complete lattice L, is investigated in detail.