Structured lattices and ground categories of L-sets
Complete lattices are considered with suitable families of lattice morphisms that provide a structure (L,Φ), useful to characterize ground categories of L-sets by means of powerset operators associated to morphisms of these categories. The construction of ground categories and powerset operators p...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2783 |
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| author | A. Frascella C. Guido |
| author_facet | A. Frascella C. Guido |
| author_sort | A. Frascella |
| collection | DOAJ |
| description | Complete lattices are considered with suitable families of lattice morphisms that provide a structure (L,Φ), useful to characterize ground categories of L-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 L-sets that includes all possible ground categories on a structured lattice (L,Φ) 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. |
| format | Article |
| id | doaj-art-14694e6c08d14dc7b8f1b7768b279479 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-14694e6c08d14dc7b8f1b7768b2794792025-02-03T05:53:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005172783280310.1155/IJMMS.2005.2783Structured lattices and ground categories of L-setsA. Frascella0C. Guido1Department of Mathematics “Ennio De Giorgi”, University of Lecce, P.O. Box 193, Lecce 73100, ItalyDepartment of Mathematics “Ennio De Giorgi”, University of Lecce, P.O. Box 193, Lecce 73100, ItalyComplete lattices are considered with suitable families of lattice morphisms that provide a structure (L,Φ), useful to characterize ground categories of L-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 L-sets that includes all possible ground categories on a structured lattice (L,Φ) 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.http://dx.doi.org/10.1155/IJMMS.2005.2783 |
| spellingShingle | A. Frascella C. Guido Structured lattices and ground categories of L-sets International Journal of Mathematics and Mathematical Sciences |
| title | Structured lattices and ground categories of L-sets |
| title_full | Structured lattices and ground categories of L-sets |
| title_fullStr | Structured lattices and ground categories of L-sets |
| title_full_unstemmed | Structured lattices and ground categories of L-sets |
| title_short | Structured lattices and ground categories of L-sets |
| title_sort | structured lattices and ground categories of l sets |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2783 |
| work_keys_str_mv | AT afrascella structuredlatticesandgroundcategoriesoflsets AT cguido structuredlatticesandgroundcategoriesoflsets |