  A Quillen model structure is presented by an interacting pair of weak
factorization systems. We prove that in the world of locally presentable
categories, any weak factorization system with accessible functorial
factorizations can be lifted along either a left or a right adjoint. It follows
that accessible model structures on locally presentable categories - ones
admitting accessible functorial factorizations, a class that includes all
combinatorial model structures but others besides - can be lifted along either
a left or a right adjoint if and only if an essential "acyclicity" condition
holds. A similar result was claimed in a paper of Hess-Kedziorek-Riehl-Shipley,
but the proof given there was incorrect. In this note, we explain this error
and give a correction, and also provide a new statement and a different proof
of the theorem which is more tractable for homotopy-theoretic applications.
