On fuzzification of the notion of quantaloid

Solovyov, Sergey A.

Kybernetika, Tome 46 (2010) no. 6, pp. 1025-1048

Abstract (VO)

The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of $\bigvee$-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 the end of the paper, we prove that the category of quantale algebroids has a monoidal structure given by tensor product.

Détail

Classification : 03E72, 06F07, 16G99, 18A40, 18B99
Keywords: many-value topology; monadic category; nucleus; quantale; quantale algebra; quantale algebroid; quantale module; quantaloid; tensor product

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