On fuzzification of the notion of quantaloid

Sergey A. Solovyov

Kybernetika (2010)

  • Volume: 46, Issue: 6, page 1025-1048
  • ISSN: 0023-5954

Abstract

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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 ⋁ -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.

How to cite

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Solovyov, Sergey A.. "On fuzzification of the notion of quantaloid." Kybernetika 46.6 (2010): 1025-1048. <http://eudml.org/doc/196866>.

@article{Solovyov2010,
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.},
author = {Solovyov, Sergey A.},
journal = {Kybernetika},
keywords = {many-value topology; monadic category; nucleus; quantale; quantale algebra; quantale algebroid; quantale module; quantaloid; tensor product; many-valued topology; monadic category; nucleus; quantale algebra; quantale algebroid; quantale module; quantaloid; tensor product},
language = {eng},
number = {6},
pages = {1025-1048},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On fuzzification of the notion of quantaloid},
url = {http://eudml.org/doc/196866},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Solovyov, Sergey A.
TI - On fuzzification of the notion of quantaloid
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 6
SP - 1025
EP - 1048
AB - 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.
LA - eng
KW - many-value topology; monadic category; nucleus; quantale; quantale algebra; quantale algebroid; quantale module; quantaloid; tensor product; many-valued topology; monadic category; nucleus; quantale algebra; quantale algebroid; quantale module; quantaloid; tensor product
UR - http://eudml.org/doc/196866
ER -

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