On Categorification (original) (raw)

Abstract

We review several known categorification procedures, and introduce a functorial categorification of group extensions with applications to non-abelian group cohomology. Categorification of acyclic models and of topological spaces are briefly mentioned.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (17)

  1. Crane, L., Frenkel, I., Four dimensional topological quantum field theory, Hopf categories, and canonical bases, J. Math. Phys. 35 (1994), 5136-5154.
  2. Crane, L., Clock and category: is quantum gravity algebraic?, J. Math. Phys. 36 (1995), 6180-6193.
  3. Baez, J. C., Dolan, J., Categorification, preprint math.QA/9802029, (1998).
  4. Davydov, A. A., On some Hochschild cohomology classes of fusion algebras, math.QA/9711025, (1997).
  5. Baez, J. C., Neuchl, M., Higher-dimensional algebra I: Braided monoidal 2-categories, Adv. Math. 121 (1996), 196-244.
  6. Saavedra, R., N., "Categories Tannakiennes", L.N.M., Vol.265 (1972), Springer-Verlag, Berlin -Hei- delberg -New York.
  7. Davydov, A.A., "Twisting of monoidal structures," preprint q-alg/9703001.
  8. Ionescu, L., On Parity complexes and non-abelian cohomology, preprint math.CT/9809068, 1998.
  9. Eilenberg, S., MacLane, S., General theory of natural equivalences, Trans. Amer. Math. Soc., Vol 58 (1945), pp. 231-294, Eilenberg-Mac Lane: Collected Works, pp. 99-162, Academic Press, Inc., 1986.
  10. Mac Lane, S., Categories for the working mathematician, Springer-Verlag, 1971.
  11. Frőlich, J., Quantum groups, quantum categories and quantum field theory, Lecture Notes in Mathe- matics, 1542, Springer-Verlag, Berlin, 1993.
  12. Crane, L., Yetter, D. Examples of categorification, preprint math.QA/9607028, (1996).
  13. Eilenberg, S., MacLane, S., Cohomology Theory in Abstract Groups, II, Group Extensions with a non-Abelian kernel, Annals of Mathematics, Vol. 48, No.2, April 1947, pp. 326-341.
  14. Brown, Ronald, From groups to groupoids: a brief survey, Bull. London Math. Soc. 19 (1987), 113-134.
  15. Segal, Graeme, Classifying spaces and spectral sequences, Publ. math. I.H.E.S, Vol. 34, (1968), pp. 105-112.
  16. Milnor, John, The geometric realization of a semi-simplicial complex, Annals of Mathematics, Vol. 65, no.2, March, 1957, pp. 357-362.
  17. Mathematics Department, Kansas State University, Manhattan, Kansas 66502 E-mail address: luciani@math.ksu.edu