Suppose we have a commutative square of simplicial sets such that: The left-most vertical map is a cofibration and the right-most vertical map is a weak equivalence (Joyal) between infty-categories. It obvious that one can find a solution to this lifting problem in the homotopy category of Set_{\Delta} with respect to the Joyal model structure.
Can I lift this solution to the original commutative square?
Can I lift this solution to the original commutative square?