. A [*finitary $0$-representation*]{} of ${{\sc\mbox{C}\hspace{0.0pt}}}$ is a $0$-semifunctor $\mathbf{M}: {{\sc\mbox{C}\hspace{0.0pt}}}\rightarrow \mathfrak{A}_{\Bbbk}$. An [*abelian $0$-representation*]{} of ${{\sc\mbox{C}\hspace{0.0pt}}}$ is a $0$-semifunctor $\mathbf{M}: {{\sc\mbox{C}\hspace{0.0pt}}}\rightarrow \mathfrak{