On Examples and Classification of Frobenius Objects in Rel

Abstract

We give some new examples of Frobenius objects in the category of sets and relations $\text{Rel}$. One example is a groupoid with a twisted counit. Another example is the set of conjugacy classes of a group. We also classify Frobenius objects in $\text{Rel}$ with two or three elements, and we compute the associated surface invariants using the partition functions of the corresponding TQFTs.

18 pages, 3 figures, 4 tables