  We prove an adjoint functor theorem in the setting of categories enriched in
a monoidal model category $\mathcal V$ admitting certain limits. When $\mathcal
V$ is equipped with the trivial model structure this recaptures the enriched
version of Freyd's adjoint functor theorem. For non-trivial model structures,
we obtain new adjoint functor theorems of a homotopical flavour - in
particular, when $\mathcal V$ is the category of simplical sets we obtain a
homotopical adjoint functor theorem appropriate to the $\infty$-cosmoi of Riehl
and Verity. We also investigate accessibility in the enriched setting, in
particular obtaining homotopical cocompleteness results for accessible
$\infty$-cosmoi.
