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Kybernetika 46 no. 6, 1025-1048, 2010

On fuzzification of the notion of quantaloid

Sergey A. Solovyov

Abstract:

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.

Keywords:

many-value topology, monadic category, nucleus, quantale, quantale algebra, quantale algebroid, quantale module, quantaloid, tensor product

Classification:

06F07, 03E72, 16G99, 18B99, 18A40

paper.pdf

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