References

  1. Samson Abramsky & Radha Jagadeesan (1994): New Foundations for the Geometry of Interaction. Inf. Comput. 111(1), pp. 53–119, doi:10.1006/inco.1994.1041.
  2. R. F. Blute, J. R. B. Cockett & R. A. G. Seely (2006): Differential categories. Mathematical structures in computer science 16(06), pp. 1049–1083, doi:10.1017/S0960129506005676.
  3. R. F. Blute, J. R. B. Cockett & R. A. G. Seely (2009): Cartesian differential categories. Theory and Applications of Categories 22(23), pp. 622–672.
  4. R. F. Blute, R. B. B. Lucyshyn-Wright & K. O'Neill (2016): Derivations in codifferential categories. Cahiers de Topologie et Géométrie Différentielle Catégoriques 57, pp. 243–280.
  5. R. F. Blute, P. Panangaden & R. A. G. Seely (1994): Fock space: a model of linear exponential types. Manuscript, revised version of the MFPS paper above.
  6. J. R. B. Cockett & G. S. H. Cruttwell (2014): Differential Structure, Tangent Structure, and SDG. Applied Categorical Structures 22(2), pp. 331–417, doi:10.1007/s10485-013-9312-0.
  7. J. R. B. Cockett & J-S. P. Lemay (2018): Integral categories and calculus categories. Mathematical Structures in Computer Science, pp. 1–66, doi:10.1017/S0960129518000014.
  8. J Robin B Cockett, Geoff S H Cruttwell & Jonathan D Gallagher (2011): Differential restriction categories. Theory and Applications of Categories 25(21), pp. 537–613.
  9. Robin Cockett, Cole Comfort & Priyaa Srinivasan (2018): The Category CNOT. In: Bob Coecke & Aleks Kissinger: Proceedings 14th International Conference on Quantum Physics and Logic, Nijmegen, The Netherlands, 3-7 July 2017, Electronic Proceedings in Theoretical Computer Science 266. Open Publishing Association, pp. 258–293, doi:10.4204/EPTCS.266.18.
  10. T. Ehrhard (2017): An introduction to Differential Linear Logic: proof-nets, models and antiderivatives. Mathematical Structures in Computer Science, pp. 1–66, doi:10.1017/S0960129516000372.
  11. Roger Fenn & Vladimir Turaev (2007): Weyl algebras and knots. Journal of Geometry and Physics 57(5), pp. 1313 – 1324, doi:10.1016/j.geomphys.2006.10.002. Available at http://www.sciencedirect.com/science/article/pii/S039304400600132X.
  12. M. Fiore (2015): An axiomatics and a combinatorial model of creation/annihilation operators. arXiv preprint arXiv:1506.06402.
  13. R. Geroch (1985): Mathematical Physics. Chicago Lectures in Physics. University of Chicago Press.
  14. A. Hadzihasanovic (2017): The algebra of entanglement and the geometry of composition.. University of OXford.
  15. M. Hasegawa (2009): On traced monoidal closed categories. Mathematical Structures in Computer Science 19(2), pp. 217–244, doi:10.1017/S096012950800718.
  16. Masahito Hasegawa (1997): Recursion from cyclic sharing: Traced monoidal categories and models of cyclic lambda calculi. In: Typed Lambda Calculi and Applications. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 196–213, doi:10.1007/3-540-62688-3_37.
  17. Masahito Hasegawa, Martin Hofmann & Gordon Plotkin (2008): Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories, pp. 367–385. Springer Berlin Heidelberg, Berlin, Heidelberg, doi:10.1007/978-3-540-78127-1_20.
  18. Martin Hyland & Andrea Schalk (2003): Glueing and orthogonality for models of linear logic. Theoretical Computer Science 294(1), pp. 183 – 231, doi:10.1016/S0304-3975(01)00241-9. Available at http://www.sciencedirect.com/science/article/pii/S0304397501002419. Category Theory and Computer Science.
  19. AndrŽ Joyal, Ross Street & Dominic Verity (1996): Traced monoidal categories. Mathematical Proceedings of the Cambridge Philosophical Society 119(3), pp. 447Ð468, doi:10.1017/S0305004100074338.
  20. Jim Laird, Giulio Manzonetto & Guy McCusker (2011): Constructing Differential Categories and Deconstructing Categories of Games. In: Luca Aceto, Monika Henzinger & Jiří Sgall: Automata, Languages and Programming. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 186–197, doi:10.1007/978-3-642-10672-9_17.
  21. S. Lang (2002): Algebra, revised 3rd ed. Graduate Texts in Mathematics 211, doi:10.1007/978-1-4613-0041-0.
  22. S. Mac Lane (1971, revised 2013): Categories for the working mathematician. Springer-Verlag, New York, Berlin, Heidelberg, doi:10.1007/978-1-4612-9839-7.
  23. Paul-André Melliès, Nicolas Tabareau & Christine Tasson (2018): An explicit formula for the free exponential modality of linear logic. Mathematical Structures in Computer Science 28(7), pp. 1253–1286, doi:10.1017/S0960129516000426.
  24. P. Selinger (2011): A Survey of Graphical Languages for Monoidal Categories, pp. 289–355. Springer Berlin Heidelberg, Berlin, Heidelberg, doi:10.1007/978-3-642-12821-9_4.
  25. Jamie Vicary (2008): A Categorical Framework for the Quantum Harmonic Oscillator. International Journal of Theoretical Physics 47(12), pp. 3408–3447, doi:10.1007/s10773-008-9772-4.

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