I am reading about the Reedy model structure from Hovey's book and
I was wondering if the Reedy model structure on $\mathcal{M}^{\Delta}$ is cofibrantly generated by a small set of arrows and permits the small object argument.
I see that in theorem 5.2.5 he proves the existence of a functorial factorization by transfinite induction assuming functorial factorization on $\mathcal{M},$ so there would not be any need to apply the SOA, but I am still left wondering if the Reedy model structure can be seen as cofibrantly generated. Is there any reference for this?
Thanks in advance.