nLab
symmetric monoidal dagger-category

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Definition

A symmetric monoidal \dagger-category is a symmetric monoidal category that is also a \dagger-category for which:

  1. (fg) =f g (f \otimes g)^\dagger = f^\dagger \otimes g^\dagger for every pair of morphisms f,gf,g

  2. the associator, left and right unitors, and braiding are all unitary.

If the category is also a compact closed category in a compatible way, then it is called a dagger-compact category.

References

  • P. Selinger, Dagger compact closed categories and completely positive maps, Proceedings of the 3rd International Workshop on Quantum Programming Languages, Chicago, June 30–July 1, 2005. web

Revised on December 16, 2010 14:37:02 by Urs Schreiber (131.211.233.8)