International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2783-2803
Structured lattices and ground categories of -sets
Department of Mathematics “Ennio De Giorgi”, University of Lecce, P.O. Box 193, Lecce 73100, Italy
Received 25 April 2005
Copyright © 2005 A. Frascella and C. Guido. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Complete lattices are considered with suitable families of lattice morphisms that provide a structure , useful to characterize ground categories of -sets by means of powerset operators associated to morphisms of these categories. The construction of ground categories and powerset operators presented here extends and unifies most approaches previously considered, allowing the use of noncrisp objects and, with some restriction, the change of base. A sufficiently large category of -sets that includes all possible ground categories on a structured lattice is provided and studied, and its usefulness is justified. Many explanatory examples have been given and connection with the categories considered by J. A. Goguen and by S. E. Rodabaugh are stated.