Equalizer in the Kleisli category of the $n$-fuzzy powerset monad

Document Type : Special Issue Dedicated to Prof. Esfandiar Eslami

Authors

Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this article, we first consider the $L$-fuzzy powerset monad on a completely distributive lattice $L$. Then for $L=[n]$, we investigate the fuzzy powerset monad on $[n]$ and we introduce simple, subsimple and quasisimple $L$-fuzzy sets. Finally, we provide necessary and sufficient conditions for the existence of an equalizer of a given pair of morphisms in the Kleisli category associated to this monad. Several illustrative examples are also provided.

Keywords

Main Subjects

References

[1] Adamek, J., Herrlich, H., & Strecker, G.E. (1990). Abstract and Concrete Categories, John Wiley & Sons, Inc. http://katmat.math.uni-bremen.de/acc.
[2] Asperti, A., & Longo, G. (1991). Categories, Types and Structures, An Introduction to Category Theory for the Working Computer Scientist, Foundations of Computing Series, M.I.T. Press.
[3] Fiore, M., & Menni, M. (2005). Re ective Kleisli Subcategories of the Category of Eilenberg-Moore Algebras for Factorization Monads, Theory and Applications of Categories, Vol. 15, No. 2, 40-65. http://www.tac.mta.ca/tac/volumes/15/2/15-02.pdf.
[4] Goguen, J.A. (1967). L-fuzzy sets, J. Math. Anal. Appl., 18, 145-174. https://doi.org/10.1016/0022-247X(67)90189-8.
[5] Gran, M., & Vitale, E.M. (1999). Localizations of Maltsev Varieties, Theory and Applications of Categories, Vol. 5, No. 12, 281-291.
[6] Hosseini, S.N., & Qasemi Nezhad, Y. (2016). Equalizers in Kleisli Catogories, Cahiers de Topologie et Geometrie Di erentielle Categoriques, Vol. LVII-1, 51-76.
[7] Jay, C.B. (2007). An Introduction to Categories in Computing, University of Technology, Sydney, School of Computing Sciences, P.O. Box 123 Broadway, Australia.
[8] Manes, E.G. (1976). Algebraic Theories. Springer Verlag. https://doi.org/10.1002/zamm.19780580331.
[9] Mockor, J. (2020). Powerset Theory of Fuzzy soft Sets, Internatinal journal of Fuzzy Logic and Intelligent Systems, 20(4), 298-315. https://doi.org/10.5391/IJFIS.2020.20.4.298.
[10] Pultr, A., & Tozzi, A. (2006). Some Categorical Aspects of Information Systems and Domains, Applied Categorical Structures, 14, 135-150. https://doi.org/10.1007/s10485-006-9011-1.
[11] Szigeti, J. (1983). On Limits and Colimits in the Kleisli Category, Cahiers de topologie et geometrie di erentielle categoriques, tome 24, No. 4, 381-391. http://www.numdam.org/item?id=CTGDC 1983 24 4 381 0.
[12] Teleiko, A. (1996). On Extension of Functors to the Kleisli Category of some Weakly Normal Monads, Commentationes Mathematicae Universitatis Carolinae, Vol. 37, No. 2, 405-410. http://dml.cz/dmlcz/118844.
Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 18 June 2024

Files

History

  • Receive Date: 14 February 2024
  • Revise Date: 31 May 2024
  • Accept Date: 16 June 2024

Share

How to cite

Statistics