  The nature of superconductivity in monolayer transition metal dichalcogenides
is still an object of debate. It has already been argued that repulsive Coulomb
interactions, combined with the disjoint Fermi surfaces around the $K$, $K'$
valleys and at the $\Gamma$ point, can lead to superconducting instabilities in
monolayer NbSe$_2$. Here, we demonstrate the two bands nature of
superconductivity in NbSe$_2$. It arises from the competition of repulsive long
range intravalley and short range intervalley interactions together with Ising
spin-orbit coupling. The two distinct superconducting gaps, one for each
spin-orbit split band, consist of a mixture of s-wave and f-wave components.
Their different amplitudes are due to different normal densities of states of
the two bands at the Fermi level. Using a microscopic multiband BCS approach,
we derive and self-consistently solve the gap equation, demonstrating the
stability of nontrivial solutions in a realistic parameter range. We find a
universal behavior of the temperature dependence of the gaps and of the
critical in-plane field which is consistent with various sets of existing
experimental data.
