String diagrams for traced and compact categories are oriented 1-cobordisms

**Abstract:**

I will present an alternate conception of string diagrams as
labeled 1-dimensional oriented cobordisms, the operad of which we
denote by Cob_L, where L is the set of string labels. The axioms of
traced (symmetric monoidal) categories are fully encoded by Cob_L in
the sense that there is an equivalence between Cob_L-algebras, for
varying L, and traced categories with varying object set. The same
holds for compact (closed) categories, the difference being in terms
of variance in L. Time permitting, we will 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.