Product and Coproduct in the Category of Fuzzy Frames

Volume 14, Issue 3, pp 243-249 http://dx.doi.org/10.22436/jmcs.014.03.07

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Authors

Maryam Yaghoobi - Assistant Professor, Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, I.R.of Iran.

Abstract

Frame theory is Lattice theory applied to topology. This approach to topology takes the lattices of open sets as the basic notion-it is "point free topology". There, one investigates typical properties of lattices of open sets that can be expressed without reference to points. In this paper we generalise the concept of frame into a fuzzy frame. The category FFrm of fuzzy frame and fuzzy frame homomorphism is defined and we show that there exist products and coproducts in the category FFrm and to construct them explicitly and we conclude that the category FFrm is complete and cocomplete.

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Keywords

• Frame
• Fuzzy frame
• Product
• Coproduct
• complete
• cocomplete.

MSC

•  06D22
•  06D72
•  54A40

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