Geodesic
On fuzzification of the notion of quantaloid
Kybernetika, Tome 46 (2010) no. 6, pp. 1025-1048

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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.
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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     author = {Solovyov, Sergey A.},
     title = {On fuzzification of the notion of quantaloid},
     journal = {Kybernetika},
     pages = {1025--1048},
     publisher = {mathdoc},
     volume = {46},
     number = {6},
     year = {2010},
     mrnumber = {2797425},
     zbl = {1218.06012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_6_a8/}
}
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Solovyov, Sergey A. On fuzzification of the notion of quantaloid. Kybernetika, Tome 46 (2010) no. 6, pp. 1025-1048. http://geodesic.mathdoc.fr/item/KYB_2010__46_6_a8/