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 X
- naturality in
: for every
and
,

Naturality in Y
- dinaturality in
: for every
and 

Dinaturality in U
- vanishing I: for every
, (with
being the right unitor),

Vanishing I
- vanishing II: for every


Vanishing II
- superposing: for every
and
,

Superposing

(where
is the symmetry of the monoidal category).
Yanking