3 October 2017
2:30 - 3:30   David Spivak
String diagrams for traced and compact categories are oriented 1-cobordisms

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.