  We investigate the proximity-induced exchange coupling in transition-metal
dichalcogenides (TMDCs), originating from spin injector geometries composed of
hexagonal boron-nitride (hBN) and ferromagnetic (FM) cobalt (Co) or nickel
(Ni), from first-principles. We employ a minimal tight-binding Hamiltonian that
captures the low energy bands of the TMDCs around K and K' valleys, to extract
orbital, spin-orbit, and exchange parameters. The TMDC/hBN/FM heterostructure
calculations show that due to the hBN buffer layer, the band structure of the
TMDC is preserved, with an additional proximity-induced exchange splitting in
the bands. We extract proximity exchange parameters in the 1--10 meV range,
depending on the FM. The combination of proximity-induced exchange and
intrinsic spin-orbit coupling (SOC) of the TMDCs, leads to a valley
polarization, translating into magnetic exchange fields of tens of Tesla. The
extracted parameters are useful for subsequent exciton calculations of TMDCs in
the presence of a hBN/FM spin injector. Our calculated absorption spectra show
large splittings for the exciton peaks; in the case of MoS$_2$/hBN/Co we find a
value of about 8 meV, corresponding to about 50 Tesla external magnetic field
in bare TMDCs. The reason lies in the band structure, where a hybridization
with Co $d$ orbitals causes a giant valence band exchange splitting of more
than 10 meV. Structures with Ni do not show any $d$ level hybridization
features, but still sizeable proximity exchange and exciton peak splittings of
around 2 meV are present in the TMDCs.
