Traced monoidal category
In category theory, a traced monoidal category is a category with some extra structure which gives a reasonable notion of feedback.
A traced symmetric monoidal category is a symmetric [monoidal category] C together with a family of functions
called a trace, satisfying the following conditions:
- naturality in : for every and,
- naturality in : for every and,
- dinaturality in : for every and
[Image:Trace diagram vanishing.svg|thumb|center|400px|Vanishing I]
- vanishing II: for every
- superposing: for every and,
- yanking:
[Image:Trace diagram yanking.svg|thumb|center|400px|Yanking]
Properties
- Every compact closed category admits a trace.
- Given a traced monoidal category C, the Int construction generates the free compact closure Int of C.