Examples of categorification

Louis Crane; David N. Yetter

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1998)

  • Volume: 39, Issue: 1, page 3-25
  • ISSN: 1245-530X

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Crane, Louis, and Yetter, David N.. "Examples of categorification." Cahiers de Topologie et Géométrie Différentielle Catégoriques 39.1 (1998): 3-25. <http://eudml.org/doc/91599>.

@article{Crane1998,
author = {Crane, Louis, Yetter, David N.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {Grothendieck rig construction; tensor and bitensor categories; Hopf algebras; topological quantum field theories},
language = {eng},
number = {1},
pages = {3-25},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Examples of categorification},
url = {http://eudml.org/doc/91599},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Crane, Louis
AU - Yetter, David N.
TI - Examples of categorification
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1998
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 39
IS - 1
SP - 3
EP - 25
LA - eng
KW - Grothendieck rig construction; tensor and bitensor categories; Hopf algebras; topological quantum field theories
UR - http://eudml.org/doc/91599
ER -

References

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  1. [1] J. Barrett and B. Westbury, "Spherical Categories," (preprint) (1992). Zbl0930.18004MR1686423
  2. [2] V. Chari and A. Pressley, A Guide to Quantum Groups, Cambridge Univ. Press (1994). Zbl0839.17009MR1300632
  3. [3] L. Crane, "Clock and Category: Is Quantum Gravity Algebraic?" J. Math. Phys.36 (11) (1995) 6180-6193. Zbl0848.57035MR1355904
  4. [4] L. Crane and I. Frenkel, "Four-dimensional Topological Quantum Field Theory, Hopf Categories, and the Canonical Bases," J. Math. Phys.35 (10) (1994) 5136-5145. Zbl0892.57014MR1295461
  5. [5] L. Crane and D.N. Yetter, "On Algebraic Structures Implicit in Topological Quantum Field Theories," J. Knot Th. and Ram. (to appear). Zbl0935.57025
  6. [6] L. Crane and D.N. Yetter, "A Categorical Construction of 4D Topological Quantum Field Theories," in Quantum Topology (L.H. Kauffman and R.A. Baadhio, eds.) World Scientific (1993) 120-130. Zbl0841.57030
  7. [7] L. Crane and D.N. Yetter, "Deformations of (Bi)tensor Categories" (in preparation). Zbl0916.18005
  8. [8] L. Crane, L.H. Kauffman and D.N. Yetter, "State-Sum Invariants of 4-Manifolds," J. Knot Th. and Ram. (to appear). Zbl0883.57021MR1452438
  9. [9] P. Deligne, "Catégories Tannakiennes," in The Grothendieck Festschrift, Volume II (P. Cartier, et al. eds.) Birkhäuser (1990) 111-196. Zbl0727.14010MR1106898
  10. [10] R. Dijkgraaf, V. Pasquier and P. Roche, "Quasi-Hopf Algebras, Group Cohomology and Orbifold Models," in Integrable Models and Quantum Groups (M. Carfora et al. eds.) World Scientific (1992). Zbl0925.16024MR1178543
  11. [11] R. Dijkgraaf and E. Witten, "Topological Gauge Theories and Group Cohomology," Comm. Math. Phys.129 (2) (1990) 393-429. Zbl0703.58011MR1048699
  12. [12] M.M. Kapranov and V.A. Voevodsky, "2-Categories and Zamolodchikov Tetrahedral Equations," Proceedings of Symposia in Pure Mathematics56 (2) (1994) 177-259. Zbl0809.18006MR1278735
  13. [13] R. Gordon, A.J. Power, and R. Street, "Coherence for Tricategories" (preprint) (1993). Zbl0836.18001MR1261589
  14. [14] S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag (1971). Zbl0232.18001MR1712872
  15. [15] S. Majid, "Quasitriangular Hopf Algebras and Yang-Baxter Equations," Int. J. of Mod. Phys.A5 (1) (1990) 1-91. Zbl0709.17009MR1027945
  16. [16] M. Wakui, "On Dijkgraaf-Witten Invariant for 3-Manifolds," Osaka J. of Math.29 (4) (1992) 675-696. Zbl0786.57008MR1192735
  17. [17] D.N. Yetter, "Topological Quantum Field Theories Associated to Finite Groups and Crossed G-Sets," J. Knot Th. and Ram.1 (1) (1992) 1-20. Zbl0770.57010MR1155090
  18. [18] D.N. Yetter, "Categorical Linear Algebra—A Setting for Questions for Physics and Low-Dimensional Topology," (preprint) (1993). 

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