With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
A symmetric monoidal $\dagger$-category is a symmetric monoidal category that is also a $\dagger$-category for which:
$(f \otimes g)^\dagger = f^\dagger \otimes g^\dagger$ for every pair of morphisms $f,g$
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.
Last revised on December 16, 2010 at 14:37:02. See the history of this page for a list of all contributions to it.