  We investigate superconducting pairing driven by electron-electron
interactions in a theoretical model for monolayer MoS$_2$ with the
temperature-flow functional renormalization group(fRG). At low doping, the
dominant instability is toward odd-parity pairing with $f$-wave
Mo-nearest-neighbor structure. We compute the fRG phase diagram versus electron
doping below the van Hove filling of the conduction band. In the
superconducting regime, the critical temperature grows with doping, comparable
to the experiments. Near van Hove filling the system favors a ferromagnetic
state. We demonstrate that the triplet pairing is driven by ferromagnetic
fluctuations and that the multiorbital nature of the conduction band as well as
the Hund's coupling appear crucial in making the physics of MoS$_2$ different
from e.g. doped graphene.
