  Using the notion of companion introduced in a previous paper with Lack, we
recover all the known dualities involving accessible categories with a class of
limits, as instances of a general duality theorem. These include the
Gabriel-Ulmer duality for locally finitely presentable categories, Diers
duality for locally finitely multipresentable categories, the Hu-Tholen duality
for locally finitely polypresentable categories, and Hu's duality for weakly
locally finitely presentable categories. In doing so, we also extend these to
the enriched setting and discuss new dualities that arise when the class of
limits taken into consideration is weakly sound.
