  We give an alternate conception of string diagrams as labeled 1-dimensional
oriented cobordisms, the operad of which we denote by Cob/O, where O is the set
of string labels. The axioms of traced (symmetric monoidal) categories are
fully encoded by Cob/O in the sense that there is an equivalence between
(Cob/O)-algebras, for varying O, and traced categories with varying object set.
The same holds for compact (closed) categories, the difference being in terms
of variance in O. As a consequence of our main theorem, we give a
characterization of the 2-category of traced categories solely in terms of
those of monoidal and compact categories, without any reference to the usual
structures or axioms of traced categories. In an appendix we offer a complete
proof of the well-known relationship between the 2-category of monoidal
categories with strong monoidal functors and the 2-category of monoidal
categories whose object set is free with strict functors; similarly for traced
and compact categories.
