  We present $\texttt{matryoshka}$, a suite of neural network based emulators
and accompanying Python package that have been developed with the goal of
producing fast and accurate predictions of the nonlinear galaxy power spectrum.
The suite of emulators consists of four linear component emulators, from which
fast linear predictions of the power spectrum can be made, allowing all
nonlinearities to be included in predictions from a nonlinear boost component
emulator. The linear component emulators includes an emulator for the matter
transfer function that produces predictions in $\sim 0.0004 \ \mathrm{s}$, with
an error of $<0.08\%$ (at $1\sigma$ level) on scales $10^{-4} \ h \
\mathrm{Mpc}^{-1}<k<10^1 \ h \ \mathrm{Mpc}^{-1}$. In this paper we demonstrate
$\texttt{matryoshka}$ by training the nonlinear boost component emulator with
analytic training data calculated with HALOFIT, that has been designed to
replicate training data that would be generated using numerical simulations.
Combining all the component emulator predictions we achieve an accuracy of $<
0.75\%$ (at $1\sigma$ level) when predicting the real space nonlinear galaxy
power spectrum on scales $0.0025 \ h \ \mathrm{Mpc}^{-1}<k<1 \ h \
\mathrm{Mpc}^{-1}$. We use $\texttt{matryoshka}$ to investigate the impact of
the analysis setup on cosmological constraints by conducting several full shape
analyses of the real space galaxy power spectrum. Specifically we investigate
the impact of the minimum scale (or $k_\mathrm{max}$), finding an improvement
of $\sim 1.8\times$ in the constraint on $\sigma_8$ by pushing $k_\mathrm{max}$
from $k_\mathrm{max}=0.25 \ h \ \mathrm{Mpc}^{-1}$ to $k_\mathrm{max}=0.85 \ h
\ \mathrm{Mpc}^{-1}$, highlighting the potential gains when using clustering
emulators such as $\texttt{matryoshka}$ in cosmological analyses.
