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On the Factorization Theorem of a Monotone Morphism in a Topos

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Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

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Abstract

In this paper, we investigate the factorization of a monotone morphism between two partially ordered objects in an arbitrary elementary topos by means of diagram proof. And then a new factorization theorem in an arbitrary elementary topos which is similar to the classical one is obtained.

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References

  1. Isbell, J.R.: Atomless parts of spaces. Math. Scand. 31, 5–32 (1972)

    MathSciNet  MATH  Google Scholar 

  2. Isbell, J.R.: First steps in descriptive theory of locales. Trans. Amer. Math. Soc. 327(1), 353–371 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Johnstone, P.T.: Sketches of an Elephant, A Topos Theory Compendium. Oxford University Press, Oxford (2002)

    Google Scholar 

  4. Johnstone, P.T.: Stone Spaces. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

  5. Johnstone, P.T., Joyal, A.: Continuous categories and exponentiable toposes. J. Pure Appl. Algebra 25(3), 255–296 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  6. Joyal, A., Tierney, M.: An extension of the Galois theory of Grothendieck. Mem. Amer. Math. Soc. 51(309), 71 (1984)

    MathSciNet  Google Scholar 

  7. Mac, L.S.: Categories for the Working Mathematician. Springer, New York (1971)

    MATH  Google Scholar 

  8. Mac, L.S., Moerdijk, I.: Sheaves in Geometry and Logic. Springer, New York (1994)

    Google Scholar 

  9. Wei, H., Yingming, L.: Steenrod’s theorem for locales. Math. Proc. Cambridge Philos. Soc. 124(2), 305–307 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wei, H.: Category Theory. Science Press, Beijing (2006) (in Chinese)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics, HuaiBei Normal University, HuaiBei, AnHui, 235000, P.R. China

    Tao Lu

  2. School of Information Science and Engineering, Rizhao Polytechnic, Rizhao, ShanDong, 276826, P.R. China

    Hong Lu

Authors
  1. Tao Lu
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  2. Hong Lu
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Lu, T., Lu, H. (2011). On the Factorization Theorem of a Monotone Morphism in a Topos. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_85

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_85

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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