A necessary and sufficient condition for induced model structures

@article{Hess2015ANA,
  title={A necessary and sufficient condition for induced model structures},
  author={Kathryn Hess and Magdalena Kȩdziorek and Emily Riehl and Brooke E. Shipley},
  journal={Journal of Topology},
  year={2015},
  volume={10}
}
A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically much harder is to lift the cofibrations and weak equivalences along a left adjoint. For either technique to define a valid model category, there is a well‐known necessary ‘acyclicity’ condition. We show that for a broad class of accessible model structures — a generalization introduced here of the well… 
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