Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A STUDY ON THE QUASI TOPOS

  • Kim, Ig Sung (Department of Data Information Sangji University)
  • Received : 2019.07.23
  • Accepted : 2020.03.04
  • Published : 2020.03.30
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Abstract

Category F Rel of fuzzy sets and relations does not form a topos. J. Harding, C. Walker and E. Walker [3] showed that FRel has a tensor product and V. Durov [1] introduced basic definitions related to the notion of vectoid endowed with a tensor product. In this paper, we show that FRel forms a quasi topos. Also we show that there are quasi power objects in FRel. And by the use of the concepts of FRel and quasi topos, we get the logic operators of FRel. Moreover, we show that FRel forms a vectoid.

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References

  1. V. Durov, Classifying Vectoid and Operad Kinds, Proceedings of the Steklov Institude of Math 2011, V. 273, pp. 48-63. https://doi.org/10.1134/S0081543811040055
  2. R. Goldblatt, Topoi, North-Holland, 1984.
  3. J. Harding, C. Walker and E. Walker, Categories with fuzzy sets and relations, Fuzzy Sets and Systems (2013), 1-17.
  4. P. T. Johnstone, Topos Theory, Academic Press, N. Y., 1977.
  5. X. Yuan, Comparisons between Category Fuz and Category Set, J. of fuzzy Math. 5 (4) (1997).
  6. X. Yuan and E. S. Lee, Category Fuz, Wtopos and Category FuzFuz, J. of Math. Anal. and Appl. 201 (1996), 489-501. https://doi.org/10.1006/jmaa.1996.0269
  7. X. Yuan, H. Li and E. S. Lee, Categories of fuzzy sets and weak topos, Fuzzy Sets and Systems 127 (2002), 291-297. https://doi.org/10.1016/S0165-0114(01)00119-1