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A note on the biadjunction between 2-categories of traced monoidal categories and tortile monoidal categories


We illustrate a minor error in the biadjointness result for 2-categories of traced monoidal categories and tortile monoidal categories stated by Joyal, Street and Verity. We also show that the biadjointness holds after suitably changing the definition of 2-cells.

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[1]Blute, R. F., Cockett, J. R. B. and Seely, R. A. G.Feedback for linearly distributive categories: traces and fixpoints. J. Pure Appl. Algebra 154 (2000), 2769.
[2]Hasegawa, M., Hofmann, M. and Plotkin, G. D. Finite dimensional vector spaces are complete for traced symmetric monoidal categories. In Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Lecture Notes in Comput. Sci. vol. 4800 (Springer-Verlag, 2008), pp. 367385.
[3]Joyal, A. and Street, R.Braided tensor categories. Adv. Math. 102 (1993), 2078.
[4]Joyal, A., Street, R. and Verity, D.Traced monoidal categories. Math. Proc. Cam. Phil. Soc. 119 (1996), 447468.
[5]Shum, M.-C.Tortile tensor categories. J. Pure Appl. Algebra 93 (1994), 57110.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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