Traces on ideals in pivotal categories

Abstract

We construct invariants of $\mathcal{C}$-colored spherical graphs from traces on ideals in a pivotal category $\mathcal{C}$. Then we provide a systematic approach to defining such traces from ambidextrous and spherical traces on a class of objects of $\mathcal{C}$. This extends the notion of an ambidextrous object of a braided category given by the first two authors in a previous work.