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Year 2016, Volume: 45 Issue: 3, 781 - 809, 01.06.2016
https://izlik.org/JA53TT79BH

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Quantale algebras as a generalization of lattice-valued frames

Year 2016, Volume: 45 Issue: 3, 781 - 809, 01.06.2016
https://izlik.org/JA53TT79BH

Abstract

Recently, I. Stubbe constructed an isomorphism between the categories
of right Q-modules and cocomplete skeletal Q-categories for a given
unital quantale Q. Employing his results, we obtain an isomorphism
between the categories of Q-algebras and Q-quantales, where Q is additionally
assumed to be commutative. As a consequence, we provide
a common framework for two concepts of lattice-valued frame, which
are currently available in the literature. Moreover, we obtain a convenient
setting for lattice-valued extensions of the famous equivalence
between the categories of sober topological spaces and spatial locales,
as well as for answering the question on its relationships to the notion
of stratification of lattice-valued topological spaces.

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There are 1 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Sergey A. Solovyov This is me

Publication Date June 1, 2016
IZ https://izlik.org/JA53TT79BH
Published in Issue Year 2016 Volume: 45 Issue: 3

Cite

APA Solovyov, S. A. (2016). Quantale algebras as a generalization of lattice-valued frames. Hacettepe Journal of Mathematics and Statistics, 45(3), 781-809. https://izlik.org/JA53TT79BH
AMA 1.Solovyov SA. Quantale algebras as a generalization of lattice-valued frames. Hacettepe Journal of Mathematics and Statistics. 2016;45(3):781-809. https://izlik.org/JA53TT79BH
Chicago Solovyov, Sergey A. 2016. “Quantale Algebras As a Generalization of Lattice-Valued Frames”. Hacettepe Journal of Mathematics and Statistics 45 (3): 781-809. https://izlik.org/JA53TT79BH.
EndNote Solovyov SA (June 1, 2016) Quantale algebras as a generalization of lattice-valued frames. Hacettepe Journal of Mathematics and Statistics 45 3 781–809.
IEEE [1]S. A. Solovyov, “Quantale algebras as a generalization of lattice-valued frames”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 3, pp. 781–809, June 2016, [Online]. Available: https://izlik.org/JA53TT79BH
ISNAD Solovyov, Sergey A. “Quantale Algebras As a Generalization of Lattice-Valued Frames”. Hacettepe Journal of Mathematics and Statistics 45/3 (June 1, 2016): 781-809. https://izlik.org/JA53TT79BH.
JAMA 1.Solovyov SA. Quantale algebras as a generalization of lattice-valued frames. Hacettepe Journal of Mathematics and Statistics. 2016;45:781–809.
MLA Solovyov, Sergey A. “Quantale Algebras As a Generalization of Lattice-Valued Frames”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 3, June 2016, pp. 781-09, https://izlik.org/JA53TT79BH.
Vancouver 1.Sergey A. Solovyov. Quantale algebras as a generalization of lattice-valued frames. Hacettepe Journal of Mathematics and Statistics [Internet]. 2016 Jun. 1;45(3):781-809. Available from: https://izlik.org/JA53TT79BH