nLab
symmetric monoidal dagger-category

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Contents

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

Last revised on December 16, 2010 at 14:37:02. See the history of this page for a list of all contributions to it.