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From Cayley-Klein double categories to TQFT

  • Elementary Particles and Fields
  • Theory
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Abstract

New applications of categorical methods are connected with new additional structures on categories. One of such structures, the double category, is considered in this article. The Cayley-Klein double category structure is defined as generalization of the Cayley-Klein bicategory structure. It is shown that Cayley-Klein double categories exist in the topological quantum field theories (TQFT).

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References

  1. S. S. Moskaliuk, From Cayley-Klein Groups to Categories (TIMPANI Publ., Kyiv, 2006).

    MATH  Google Scholar 

  2. S. MacLane, Categories for Working Mathematician, Graduate Texts in Mathematics, no. 5 (Springer, Berlin, 1971).

    Google Scholar 

  3. S. S. Moskaliuk and A. T. Vlassov, in Proc. of the 5th Wigner Symp., Vienna, 1997 (World Sci., Singapore, 1998), p. 162.

    Google Scholar 

  4. S. S. Moskaliuk and A. T. Vlassov, Ukr. J. Phys. 43, 162 (1998).

    MathSciNet  Google Scholar 

  5. P. Deligne and J. S. Milne, Lecture Notes in Math. 900, 101 (1982).

    Article  MathSciNet  Google Scholar 

  6. P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory (Springer, Berlin, Heidelberg, New York, 1967).

    MATH  Google Scholar 

  7. J.-L. Loday, Cyclic Homology (Springer, Berlin, Heidelberg, 1992).

    MATH  Google Scholar 

  8. M. F. Atiyah, Publ. Math. Inst. Hautes Etudes Sci. (Paris) 68, 175 (1989).

    Article  Google Scholar 

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Authors and Affiliations

  1. Bogoliubov Institute for Theoretical Physics of NAS of Ukraine, Kiev, Ukraine

    S. Moskaliuk

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  1. S. Moskaliuk
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Correspondence to S. Moskaliuk.

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Moskaliuk, S. From Cayley-Klein double categories to TQFT. Phys. Atom. Nuclei 73, 485–488 (2010). https://doi.org/10.1134/S1063778810030105

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  • DOI: https://doi.org/10.1134/S1063778810030105

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