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Suppose that    F  :  N  →  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   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    (  ∞  ,  1  )   ‐categories and show that known Quillen equivalences between base model categories lift to equivalences.

A criterion for existence of right‐induced model structures