In a monoidal category, there are generally two types of ideals: thick and tensor ideals. The current paper's main focus is on ideals of the former type, which are defined on the objects of the ambient category. In the setting of a semisimple pivotal category, we introduce a particular class of pseudo-negligible morphisms and establish some related results. Moreover, given a one-sided thick ideal I of a semisimple pure pivotal category, we call I admissible when it is equipped with a one-sided trace function whose associated modified dimension is invertible on the simple objects therein. We then introduce and study a determinant function on such ideals and establish analogous properties to those of the usual determinants. As an application, we construct new topological invariants of planar graphs from these determinant functions on traced ideals.
Keywords: Diagram invariant, categorical trace, quantum determinants, pivotal category, one-sided ideal, semisimplicity
2020 MSC: 15A99, 18A05, 18E05
Theory and Applications of Categories, Vol. 45, 2026, No. 29, pp 1201-1226.
Published 2026-05-19.
TAC Home