Abstract cellularization as a cellularization with respect to a set of   objects
  Given a simplicial idempotent augmented endofunctor $F$ on a simplicial combinatorial model category $M$, under the assumption of Vopenka's principle, we exhibit a set $A$ of cofibrant objects in $M$ such that $F$ is equivalent to $\CW_A$, the cellularization with respect to $A$. 
Boris Chorny