  For any symmetric monoidal category $\mathcal{D}$, Lauda and Pfeiffer showed
the equivalence between the $\mathcal{D}$-valued open-closed 2-dimensional
TQFTs and the so-called knowledgeable Frobenius algebras (KFAs) in
$\mathcal{D}$. Each KFA in $\mathcal{D}=\mathbf{Vec}_{\mathbb{K}}$ provides a
sequence of scalars indexed by the set $\mathbb{N}^2$ of diffeomorphism classes
of connected endocobordisms of the empty set, given by evaluation by the
associated TQFT on each such cobordism class. From an arbitrary sequence
$\chi=(\chi_{g,w})_{g,w\in\mathbb{N}}$, we build a symmetric monoidal category
$\mathcal{C}_{\chi}$ -- with unit object $\textbf{1}$ satisfying
$\text{End}_{\mathcal{C}_{\chi}}(\textbf{1})\cong \mathbb{K}$ -- generated by a
KFA object affording this sequence. We then determine which sequences $\chi$
produce semisimple abelian categories $\mathcal{C}_{\chi}$ with
finite-dimensional hom-spaces. These form a family of categories interpolating
the categories of representations of automorphism groups of certain KFAs in
$\mathbf{Vec}_{\mathbb{K}}$.
