no. 1
On braiding, syllapses and symmetries
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 41 (2000) no. 1, pp. 2-74
corrigé par Erratum “On braidings, syllepses, and symmetries” 
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     volume = {41},
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     mrnumber = {1748753},
     zbl = {0945.18005},
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Crans, Sjoed. On braiding, syllapses and symmetries. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 41 (2000) no. 1, pp. 2-74. https://www.numdam.org/item/CTGDC_2000__41_1_2_0/

[1] J. Adams, "Infinite loop spaces", Princeton U. Press, Princeton, 1978. | Zbl | MR

[2] J.C. Baez and J. Dolan, Higher dimensional algebra and Topological Quantum Field Theory, Jour. Math. Phys. 36 (1995), 6073-6105. | Zbl | MR

[3] J.C. Baez and J. Dolan, Higher dimensional algebra III: n-categories and the algebra of opetopes, Adv. Math. 135 (1998), 145-206. | Zbl | MR

[4] J.C. Baez and L. Langford, 2-tangles, Lett. Math. Phys. 43 (1998), 187-197. | Zbl | MR

[5] J.C. Baez and M. Neuchl, Higher dimensional algebra I. Braided monoidal 2-categories, Adv. Math. 121 (1996), 196-244. | Zbl | MR

[6] M.A. Batanin, Monoidal globular categories as natural environment for the theory of weak n-categories, Adv. Math. 136 (1998), 39-103. | Zbl | MR

[7] L. Breen, On the classification of 2-gerbes and 2-stacks, Astérisque 225 (1994). | Zbl | MR | Numdam

[8] R. Brown and N.D. Gilbert, Algebraic models of 3-types and automorphism structures for crossed modules, Proc. London Math. Soc. 59 (1989), 51-73. | Zbl | MR

[9] S.E. Crans, "On combinatorial models for higher dimensional homotopies", Ph.D. thesis, Utrecht University, 1995.

[10] S.E. Crans, Generalized centers of braided and sylleptic monoidal 2-categories, Adv. Math. 136 (1998), 183-223. | Zbl | MR

[11] S.E. Crans, A tensor product for Gray-categories, Preprint 97/222, Macquarie University. | MR

[12] S.E. Crans, Higher dimensional Zamolodchikov and Yang-Baxter equations, in preparation.

[13] B. Day and R. Street, Monoidal bicategories and Hopf algebroids, Adv. Math. 129 (1997), 99-157. | Zbl | MR

[14] P.J. Freyd and D.N. Yetter, Braided Compact Closed Categories with Applications to Low Dimensional Topology, Adv. Math. 77 (1989), 156-182. | Zbl | MR

[15] R. Gordon, A.J. Power, and R. Street, Coherence for tricategories, Mem. Amer. Math. Soc. 117 (1995), no. 558. | Zbl | MR

[16] J.W. Gray, "Formal category theory: adjointness in 2-categories", vol. 391 of Lecture Notes in Math., Springer Verlag, New York, 1974. | Zbl | MR

[17] C. Hermida, M. Makkai, and J. Power, On weak higher dimensional categories, J. Pure Appl. Algebra (to appear). | Zbl

[18] M. Johnson, The combinatorics of n-categorical pasting, J. Pure Appl. Algebra 62 (1989), 211-225. | Zbl | MR

[19] A. Joyal, letter to A. Grothendieck, 1984.

[20] A. Joyal and R. Street, The Geometry of Tensor Calculus, I, Adv. Math. 88 (1991), 55-112. | Zbl | MR

[21] A. Joyal and R. Street, Tortile Yang-Baxter operators in tensor categories, J. Pure Appl. Algebra 71 (1991), 43-51. | Zbl | MR

[22] A. Joyal and R. Street, Braided tensor categories, Adv. Math. 102 (1993), 20-78. | Zbl | MR

[23] M.M. Kapranov and V.A. Voevodsky, Braided monoidal 2-categories, 2-vector spaces and Zamolodchikov's tetrahedra equations, draft.

[24] M.M. Kapranov and V.A. Voevodsky, 2-categories and Zamolodchikov tetrahedra equations, in "Algebraic groups and their generalizations: quantum and infinite-dimensional methods", vol. 56 of Proc. Sympos. Pure Math., pp. 177-259, Amer. Math. Soc., Providence, RI, 1994. | Zbl | MR

[25] M.M. Kapranov and V.A. Voevodsky, Braided monoidal 2-categories and Manin-Schechtman higher braid groups, J. Pure Appl. Algebra 92 (1994), 241-267. | Zbl | MR

[26] C. Kassel, "Quantum groups", vol. 155 of Graduate Texts in Math., Springer Verlag, New York, 1995. | Zbl | MR

[27] G.M. Kelly, "Basic concepts of enriched category theory", vol. 64 of London Math. Soc. Lecture Note Ser., Cambridge U. Press, 1982. | Zbl | MR

[28] G.M. Kelly and R. Street, Review of the elements of 2-categories, in "Proceedings of the Sydney Category Seminar 1973", vol. 420 of Lecture Notes in Math., pp. 75-103, Springer Verlag, New York, 1974. | Zbl | MR

[29] S. Mac Lane and R. Paré, Coherence for bicategories and indexed categories, J. Pure Appl. Algebra 37 (1985), 59-80. | Zbl | MR

[30] J.P. May, "The geometry of iterated loop-spaces", vol. 271 of Lecture Notes in Math., Springer Verlag, New York, 1972. | Zbl | MR

[31] R. Street, Parity complexes, Cahiers Topologie Géom. Différentielle Catég. 32 (1991), 315-343. | Zbl | MR | Numdam

[32] T. Trimble, The definition of tetracategory, handwritten diagrams.