A criterion for existence of right‐induced model structures

Abstract

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.