  Suppose that $F: \mathcal{N} \to \mathcal{M}$ is a functor whose target is a
Quillen model category. We give a succinct sufficient condition for the
existence of the right-induced model category structure on $\mathcal{N}$ in the
case when $F$ admits both adjoints. We give several examples, including
change-of-rings, operad-like structures, and anti-involutive structures on
infinity categories. For the last of these, we explore anti-involutive
structures for several different models of $(\infty, 1)$-categories, and show
that known Quillen equivalences between base model categories lift to
equivalences.
