  For coalgebras $C$ over a field, we study when the categories ${}^C\Mm$ of
left $C$-comodules and $\Mm^C$ of right $C$-comodules are symmetric categories,
in the sense that there is a duality between the categories of finitely
presented unitary left $R$-modules and finitely presented unitary left
$L$-modules, where $R$ and $L$ are the functor rings associated to the finitely
accessible categories ${}^C\Mm$ and $\Mm^C$.
