  Recent systematic searches for massive black holes (BHs) in local dwarf
galaxies led to the discovery of a population of faint Active Galactic Nuclei
(AGN). We investigate the agreement of the BH and AGN populations in the
Illustris, TNG, Horizon-AGN, EAGLE, and SIMBA simulations with current
observational constraints in low-mass galaxies. We find that some of these
simulations produce BHs that are too massive, and that the BH occupation
fraction at z=0 is not inherited from the simulation seeding modeling. The
ability of BHs and their host galaxies to power an AGN depends on BH and galaxy
subgrid modeling. The fraction of AGN in low-mass galaxies is not used to
calibrate the simulations, and thus can be used to differentiate galaxy
formation models. AGN fractions at z=0 span two orders of magnitude at fixed
galaxy stellar mass in simulations, similarly to observational constraints, but
uncertainties and degeneracies affect both observations and simulations. The
agreement is difficult to interpret due to differences in the masses of
simulated and observed BHs, BH occupation fraction affected by numerical
choices, and an unknown fraction of obscured AGN. Our work advocates for more
thorough comparisons with observations to improve the modeling of cosmological
simulations, and our understanding of BH and galaxy physics in the low-mass
regime. The mass of BHs, their ability to efficiently accrete gas, and the AGN
fraction in low-mass galaxies have important implications for the build-up of
the entire BH and galaxy populations with time.
