  We use the Cosmic Archaeology Tool (CAT) semi-analytical model to explore the
contribution of Population (Pop) III/II stars and active galactic nuclei (AGNs)
to the galaxy UV luminosity function (LF) evolution at $4 \leq z \leq 20$. We
compare in particular with recent JWST data in order to explore the apparent
tension between observations and theoretical models in the number density of
bright galaxies at $z \gtrsim 10$. The model predicts a star formation history
dominated by UV faint ($M_{\rm UV} > - 18$) galaxies, with a Pop III
contribution of $\lesssim 10\%$ ($\lesssim 0.5\%$) at $z \simeq 20$ ($z \simeq
10$). Stars are the primary sources of cosmic reionization, with $5 - 10 \%$ of
ionizing photons escaping into the intergalatic medium at $5 \leq z \leq 10$,
while the contribution of unobscured AGNs becomes dominant only at $z \lesssim
5$. The predicted stellar and AGN UV LFs reproduce the observational data at $5
\lesssim z \lesssim 9 - 10$. At higher redshift, CAT predicts a steeper
evolution in the faint-end slope ($M_{\rm UV} > - 18$), and a number density of
bright galaxies ($M_{\rm UV} \simeq -20$) consistent with data at $z \sim 10 -
11$, but smaller by 0.8 dex at $z \sim 12 - 13$, and 1.2 dex at $z \sim 14 -
16$, when compared to the values estimated by recent studies. Including the AGN
emission does not affect the above findings, as AGNs contribute at most to
$\lesssim 10 \%$ of the total UV luminosity at $M_{\rm UV} < - 19$ and $z
\gtrsim 10$. Interestingly, considering a gradual transition in the stellar
IMF, modulated by metallicity and redshift as suggested by recent simulations,
the model agrees with JWST data at $z \sim 12 - 13$, and the disagreement at $z
\sim 14 - 16$ is reduced to 0.5 dex.
