  We present an analysis of the galaxy stellar mass function (SMF) of 14 known
protoclusters between $2.0 < z < 2.5$ in the COSMOS field, down to a mass limit
of $10^{9.5}$ M$_{\odot}$. We use existing photometric redshifts with a
statistical background subtraction, and consider star-forming and quiescent
galaxies identified from $(NUV - r)$ and $(r - J)$ colours separately. Our
fiducial sample includes galaxies within 1 Mpc of the cluster centres. The
shape of the protocluster SMF of star-forming galaxies is indistinguishable
from that of the general field at this redshift. Quiescent galaxies, however,
show a flatter SMF than in the field, with an upturn at low mass, though this
is only significant at $\sim 2\sigma$. There is no strong evidence for a
dominant population of quiescent galaxies at any mass, with a fraction of $<
15\%$ at $1\sigma$ confidence for galaxies with log$M_{\ast}/M_{\odot} < 10.5$.
We compare our results with a sample of galaxies groups at $1 < z < 1.5$, and
demonstrate that a significant amount of environmental quenching must take
place between these epochs, increasing the relative abundance of high-mass
($\rm M > 10^{10.5} M_{\odot}$) quiescent galaxies by a factor of $\gtrsim$ 2.
However, we find that at lower masses ($\rm M < 10^{10.5} M_{\odot}$), no
additional environmental quenching is required.
