A Frobenius algebra object $A$ in a tensor category $\mathcal C$ is said to be connected if $\text{Hom}_{\mathcal C}(\mathbb{1}, A)$ is a one dimensional vector space, where $\mathbb {1} $ denotes the tensor unit of $\mathcal C$.
Can yousomeone provide examples of connected Frobenius algebras that are non-semisimple as an object of a tensor category?
