  Reflexive DG-categories were defined by Kuznetsov and Shinder as
generalisations of smooth and proper DG-categories. Over a perfect field, they
include all projective schemes and finite dimensional algebras. Smooth and
proper DG-categories are the dualizable objects in the symmetric monoidal
category of DG-categories localised at Morita equivalences. We show the
reflexive DG-categories are the reflexive objects in this monoidal category.
Using this perspective we prove that the Hochschild cohomology of a reflexive
DG-category is isomorphic to that of its derived category of cohomologically
finite modules.
