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On extended frames

Jorge Picado (1995)

Commentationes Mathematicae Universitatis Carolinae

Some aspects of extended frames are studied, namely, the behaviour of ideals, covers, admissible systems of covers and uniformities.

On fuzzification of the notion of quantaloid

Sergey A. Solovyov (2010)

Kybernetika

The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of -semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At...

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