Obstructions to coherence: Natural noncoherent associativity

Journal of Pure and Applied Algebra

Volumn 147, Issue 2, 2000, Pages 175-213

  Yanofsky, Noson S ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034708286     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(98)00138-8     Document Type: Article

References (28)

1. [1] J.C. Baez, J. Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (11) (1995) 6073-6105.
2. [2] L. Crane, D. Yetter, On algebraic structures implicit in topological quantum field theories, Kansas Univ. preprint available as hep-th/9412025.
3. [3] D.B.A. Epstein, Steenrod operations in homological algebra, Invent. Math. 1 (1966) 152-208.
4. [4] D.B.A. Epstein, Functors between tensored categories, Invent. Math. 1 (1966) 221-228.
5. [5] R. Gorden, A.J. Power, R. Street, Coherence of tricategories, Mem. Amer. Math. Soc. 117 (558) (1995).
6. [6] A. Heller, personal correspondence.
7. [7] P. Hilton, J. Pedersen, Catalan numbers, their generalization and their uses, Math. Intelligence 13 (2) (1991) 64-75.
8. [8] A. Joyal, R. Street, Braided tensor categories, Adv. Math. 102 (1993) 20-78.
9. [9] M. Kapranov, The permutoassociahedron, Mac Lane's coherence theorem and asymptotic zones for the KZ equations, J. Pure Appl. Algebra 85 (1993) 119-142.
10. [10] C. Kassel, Quantum Groups, Springer, Berlin, 1995.
11. [11] G.M. Kelley, An abstract approach to coherence, in: Coherence in Categories, Lecture Notes in Mathematics, vol. 281, Springer, Berlin, 1972, pp. 106-147.
12. [12] G.M. Kelley, A cut-elimination theorem, in: Coherence in Categories, Lecture Notes in Mathematics, vol. 281, Springer, Berlin, 1972, pp. 196-213.
13. [13] I. Kriz, J.P. May, Operads, algebras, modules and motives, Asterisque (233) (1995).
14. [14] J.-L. Loday et al. (Eds.), Operads: Proc. Renaissance Conferences, 1997, Contemporary Mathematics, vol. 202.
15. [15] R.C. Lyndon, P.E. Schupp, Combinatorial Group Theory, Springer, Berlin, 1977.
16. [16] S. Mac Lane, Natural associativity and commutativity, Rice Univ. Stud. 49 (4) (1963) 28-46.
17. [17] S. Mac Lane, Categories for the Working Mathematician, Springer, Berlin, 1971.
18. [18] S. Mac Lane, Why Commutative diagrams coincide with equivalent proofs, Contemp. Math. 13 (1982) 387-341.
19. [19] P. May, The Geometry of Iterated Loop Spaces, Lecture Notes in Mathematics, vol. 271, Springer, Berlin, 1972.
20. [20] J. Rotman, The Theory of Groups; an Introduction, Allyn and Bacon, Boston, 1973.
21. [21] S. Shnider, S. Sternberg, Quantum Groups from Coalgebras to Drinfeld Algebras, International Press Publications, 1993.
22. [22] J. Stasheff, Homotopy associativity of H-spaces I, Trans. Amer. Math. Soc. 108 (1963) 275-292.
23. [23] J. Stasheff, Differential graded Lie algebras, quasi-Hopf algebras and higher homotopy algebras, Quantum Groups Proc., Leningrad 1990, Lecture Notes in Mathematics, vol. 1510, Springer, Berlin, 1992, pp. 120-137.
24. [24] A.S. Troelstra, Lectures on linear logic, CSLI Lecture No. 29, 1992.
25. [25] N.S. Yanofsky, Obstructions to coherence: natural noncoherent associativity and tensor functors, Thesis, CUNY-Graduate Center, 1996.
26. [26] N.S. Yanofsky, Natural noncoherent braided categories, in preparation.
27. [27] D.A. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Cambridge Philos. Soc. 108 (1990) 261-290.
28. [28] G. Ziegler, Lectures on Polytopes, Springer, Berlin, 1995.