-
- 1
- S. Abramsky and B. Coecke, A categorical semantics of
quantum protocols, available at
http://www.arXiv.org/abs/quant-ph/0402130.
- 2
- M. F. Atiyah, Topological quantum field theories,
Publ. Math. IHES Paris 68 (1989), 175-186.
M. F. Atiyah, The Geometry and Physics
of Knots, Cambridge U. Press, Cambridge, 1990.
- 3
- J. Baez, Bell's inequality for C*-algebras,
Lett. Math. Phys. 13 (1987), 135-136.
- 4
- J. Baez, Spin foam models, Class. Quantum
Grav. 15 (1998), 1827-1858. Also available at
http://www.arXiv.org/abs/gr-qc/9709052.
J. Baez, An introduction to spin foam models of quantum gravity
and
BF theory, in Geometry and Quantum Physics, eds. H. Gausterer and H. Grosse, Springer, Berlin, 2000, pp. 25-93.
Also available at http://www.arXiv.org/abs/gr-qc/9905087.
- 5
- J. Baez, Higher-dimensional algebra and Planck-scale
physics, in Physics Meets Philosophy at the Planck Length, eds. Craig Callender and Nick Huggett, Cambridge U. Press, Cambridge,
2001, pp. 177-195. Also available at
http://www.arXiv.org/abs/gr-qc/9902017 and
this website.
- 6
- J. Baez and J. Dolan, Higher-dimensional algebra
and topological quantum field theory, Jour. Math. Phys. 36
(1995), 6073-6105. Also available at
http://www.arXiv.org/q-alg/9503002.
- 7
- M. Barr and C. Wells, Toposes, Triples and Theories,
Springer Verlag, Berlin, 1983. Revised and corrected version available
at
http://www.cwru.edu/artsci/math/wells/pub/ttt.html.
- 8
- J. S. Bell, On the Einstein-Podolsky-Rosen
paradox, Physics 1 (1964), 195-200.
- 9
- A. Boileau, A. Joyal, La logique des topos,
J. Symb. Logic 46 (1981), 6-16.
- 10
- D. Corfield, Towards a Philosophy of
Real Mathematics, Cambridge U. Press, Cambridge, 2003.
- 11
- M. Coste, Langage interne d'un topos,
Seminaire Bénabou, Université Paris-Nord 1972.
- 12
- R. L. Crole, Categories for Types, Cambridge
U. Press, Cambridge, 1993.
- 13
-
A. Arageorgis, J. Earman, and L. Ruetsche,
Weyling the time away: the non-unitary implementability of
quantum field dynamics on curved spacetime,
Studies in the History and Philosophy of Modern Physics,
33 (2002), 151-184.
- 14
- A. Einstein, B. Podolsky, and N. Rosen,
Can quantum-mechanical description of physical reality
be considered complete?, Phys. Rev. 47 (1935) 77.
- 15
- E. Hawkins, F. Markopoulou and H. Sahlmann,
Evolution in quantum causal histories, Class. Quant.
Grav. 20 (2003), 3839-3854. Also available at
http://www.arXiv.org/abs/hep-th/0302111.
- 16
- P. Johnstone, Toposes as theories, in
Sketches of an Elephant: A Topos Theory Compendium,
vol. 2, Oxford U. Press, Oxford, 2002, pp. 805-1088.
- 17
- A. Kanamori, The empty set, the singleton,
and the ordered pair, Bull. Symb. Logic 9 (2003),
273-298. Also available as
http://www.math.ucla.edu/~asl/bsl/0903/0903-001.ps.
- 18
- J. Lambek, From -calculus to cartesian
closed categories, in To H. B. Curry: Essays on Combinatory
Logic, Lambda Calculus and Formalism, eds. J. P. Seldin and J. R. Hindley, Academic Press, New York, 1980, pp. 375-402.
- 19
-
G. Lakoff and R. Núñez, Where Mathematics Comes From:
How the Embodied Mind Brings Mathematics into Being, Basic Books, 2000.
- 20
- J. Lambek and P. J. Scott, Introduction to
Higher-Order Categorical Logic, Cambridge U. Press, Cambridge,
1986.
- 21
- F. W. Lawvere, Functorial Semantics of
Algebraic Theories, Ph.D. Dissertation, Columbia University, 1963.
- 22
- J.-L. Loday, J. Stasheff and A. Voronov, eds.,
Operads: Proceedings of Renaissance Conferences, American
Mathematical Society, Providence, Rhode Island, 1997.
- 23
- S. Mac Lane, Natural associativity and
commutativity, Rice Univ. Stud. 49 (1963) 28-46.
- 24
- S. Mac Lane and I. Moerdijk, Sheaves in
Geometry and Logic: a First Introduction to Topos Theory,
Springer Verlag, Berlin, 1992.
- 25
- M. Markl, S. Shnider and J. Stasheff,
Operads in Algebra, Topology and Physics, American
Mathematical Society, Providence, Rhode Island, 2002.
- 26
- L. Mauri, Algebraic theories in monoidal categories,
available at
http://www.math.rutgers.edu/~mauri.
- 27
- C. McLarty, Elementary Categories,
Elementary Toposes, Clarendon Press, Oxford, 1995.
- 28
- W. Mitchell, Boolean topoi and the
theory of sets, J. Pure Appl. Alg. 2 (1972),
261-274.
- 29
- G. Segal, The definition of a conformal field theory,
in Topology, Geometry and Quantum Field Theory: Proceedings of the
2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal,
ed. U. L. Tillmann, Cambridge U. Press, 2004.
- 30
- L. Smolin, Three Roads to Quantum Gravity,
Basic Books, New York, 2001.
L. Smolin, How far are we from the theory of quantum
gravity?, available at http://www.arXiv.org/abs/hep-th/0303185.
- 31
- R. Vaas, The duel: strings versus loops, trans. M. Bojowald and A. Sen, available at
http://www.arXiv.org/abs/physics/0403112.
- 32
- W. K. Wootters and W. H. Zurek,
A single quantum cannot be cloned, Nature 299
(1982), 802-803.