  We present a post-processing catalog of globular clusters (GCs) for the $39$
most massive groups and clusters in the TNG50 simulation of the IlllustrisTNG
project (virial masses $M_{200} =[5\times 10^{12} \rm - 2 \times 10^{14}$]
M$_{\odot}$). We tag GC particles to all galaxies with stellar mass $M_* \geq
5\times10^6$ M$_{\odot}$, and we calibrate their masses to reproduce the
observed power-law relation between GC mass and halo mass for galaxies with
$M_{200} \geq 10^{11}$ M$_{\odot}$ (corresponding to $M_* \sim 10^9$
$M_{\odot}$). Here we explore whether an extrapolation of this $M_{\rm
GC}$-$M_{200}$ relation to lower-mass dwarfs is consistent with current
observations. We find a good agreement between our predicted number and
specific frequency of GCs in dwarfs with $\rm M_*=[5 \times 10^6 \rm - 10^9]$
M$_{\odot}$ and observations. Moreover, we predict a steep decline in the GC
occupation fraction for dwarfs with $M_*<10^9$ M$_{\odot}$ which agrees well
with current observational constraints. This declining occupation fraction is
due to a combination of tidal stripping in all dwarfs plus a stochastic
sampling of the GC mass function for dwarfs with $M_* < 10^{7.5}$ M$_{\odot}$.
Our simulations also reproduce available constraints on the abundance of
intra-cluster GCs in Virgo and Centaurus A. These successes provide support to
the hypothesis that the $M_{\rm GC}$-$M_{200}$ relation holds, albeit with more
scatter, all the way down to the regime of classical dwarf spheroidals in these
environments. Our GC catalogs are publicly available as part of the
IllustrisTNG data release.
