  We give some new examples of Frobenius objects in the category of sets and
relations $\textbf{Rel}$. 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 $\textbf{Rel}$ with two or three elements, and we compute
the associated surface invariants using the partition functions of the
corresponding TQFTs.
