The syntax of coherence
Yanofsky, Noson S.
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 41 (2000), p. 255-304 / Harvested from Numdam
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Publié le : 2000-01-01
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     author = {Yanofsky, Noson S.},
     title = {The syntax of coherence},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {41},
     year = {2000},
     pages = {255-304},
     mrnumber = {1805933},
     zbl = {0989.18005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2000__41_4_255_0}
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Yanofsky, Noson S. The syntax of coherence. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 41 (2000) pp. 255-304. http://gdmltest.u-ga.fr/item/CTGDC_2000__41_4_255_0/

[1] Michael Barr and Charles Wells. Category Theory for Computing Science. Prentice Hall (1990). | MR 1094561 | Zbl 0714.18001

[2] R. Blackwell, G.M. Kelly and A.J. Power. Two-dimensional monad theory. Journal of Pure and Applied Algebra 59 (1989) 1-41. | MR 1007911 | Zbl 0675.18006

[3] F. Borceux And Brian Day. Universal algebra in a closed category. Journal of Pure and Applied Algebra 16 (1980) 133-147. | MR 556156 | Zbl 0426.18004

[4] D. Bourn. Natural anadeses and catadeses. Cahiers Topo. et Geom. Diff. Vol XIV-4(1973) 1 - 45. | Numdam | MR 354808 | Zbl 0323.18003

[5] M. Bunge. Bifibration induced adjoint pairs. Reports of the Midwest Category Seminar, V (Zurich, 1970) Lecture Notes in Math Vol 195. 70 - 122. | MR 292904 | Zbl 0224.18009

[6] M. Bunge. Coherent extensions and relational algebras. Trans. Amer. Math. Soc. 197 (1974) 355 - 390. | MR 344305 | Zbl 0358.18004

[7] P. Freyd. Algebra valued functors in general and tensor products in particular. Colloquium Mathematicum XIV (1996) 89-106. | MR 195920 | Zbl 0144.01003

[8] John W. Gray. Quasi-Kan extensions for 2-categories. Bulletin of the A.M.S. Vol. 80, Number 1, January (1974) 142-147. | MR 340369 | Zbl 0358.18005

[9] John W. Gray. Formal Category Theory: Adjointness for 2-categories. Springer-Verlag LNM391 (1974). | MR 371990 | Zbl 0285.18006

[10] John W. Gray. 2-Algebraic theories and triples, Cahiers Topologie Geom. Differentielle XIV (1974), 178 - 180.

[11] John W. Gray. Coherence for the Tensor Product of 2-Categories, and Braid Groups. Algebra, topology, and category theory (a collection of papers in honor of Samuel Eilenberg), Academic Press, New York, 1976. 63-76. | MR 412252 | Zbl 0391.18007

[12] A. Joyal and R. Street. Braided tensor categories,revised. Macquarie Math. Report no 86081.

[13] A. Joyal and R. Street. Braided tensor categories. Adv. Math.102 (1993) 20-78. | MR 1250465 | Zbl 0817.18007

[14] C. Kassel. Quantum Groups, Vol 155 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. | MR 1321145 | Zbl 0808.17003

[15] F.W. Lawvere. Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963) 869-872. | MR 158921 | Zbl 0119.25901

[16] F.W. Lawvere. Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories, Springer Lecture Notes in Mathematics No. 61, Springer-Verlag (1968), 41-61. | MR 231882 | Zbl 0204.33802

[17] F.W. Lawvere. Ordinal Sums and Equational Doctrines, Springer Lecture Notes in Mathematics No. 80, Springer-Verlag (1969), 141-155. | MR 240158 | Zbl 0165.03204

[18] M. Markl. Models for operads, Comm. Algebra 24 (1996), no.4 1471-1500. | MR 1380606 | Zbl 0848.18003

[19] S. Maclane. Naural associativity and commutativity. Rice Univ. Studies 49 (1963) 28-46. | MR 170925 | Zbl 0244.18008

[20] J.L. Macdonald and A. Stone. Soft Adjunction between 2-categories. Journal of Pure and Applied Algebra 60 (1989) 155-203. | MR 1020715 | Zbl 0686.18003

[21] R. Seely. Modeling computations: a 2-categorical approach. Proc. Symposium on Logic in Computer Science, 1987 (Computer Society of the IEEE, 1987) 65-71.

[22] R. Street. Two constructions on lax functors. Cahiers Topo. et Geom. Diff. Vol XIII - 3 (1972) 217 - 264. | Numdam | MR 347936 | Zbl 0252.18008

[23] U. Tillmann. Discrete models for the category of Riemann surfaces. Math. Proc. Camb. Phil. Soc. 121,39 (1997). | MR 1418359 | Zbl 0905.55011

[24] A. Voronov. The Swiss-Cheese Operad. Preprint available as math.QA/980737. July 1998. | MR 1718089

[25] E.G. Wagner. Algebraic semantics. Handbook of logic in computer science, vol 3. Pg 323 - 393 (1994). | MR 1365751

[26] N.S. Yanofsky. Obstructions to Coherence: Natural Noncoherent Associativity and Tensor Functors Thesis of City University of New York (1996).

[27] N.S. Yanofsky. Obstructions to Coherence: Natural Noncoherent Associativity. Accepted for publication Journal of Pure and Applied Algebra. Available in Quantum Algebra http://xxx.lanl.gov/QA/9804106. | Zbl 0973.18004

[28] N.S. Yanofsky. Natural Noncoherent Commutativity. in preparation.

[29] N.S. Yanofsky. Relative Coherence Theory. work in progress.

[30] D.A. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Camb. Phil. Soc. (1990), 108, 261-290. | MR 1074714 | Zbl 0712.17014