  We investigate proximity-induced superconductivity in monolayers of
transition metal dichalcogenides (TMDs) in the presence of an externally
generated exchange field. A variety of superconducting order parameters is
found to emerge from the interplay of magnetism and superconductivity, covering
the entire spectrum of possibilities to be symmetric or antisymmetric with
respect to the valley and spin degrees of freedom, as well as even or odd in
frequency. More specifically, when a conventional \emph{s}-wave superconductor
with singlet Copper pairs is tunnel-coupled to the TMD layer, both spin-singlet
and triplet pairings between electrons from the same and opposite valleys arise
due to the combined effects of intrinsic spin-orbit coupling and a
magnetic-substrate-induced exchange field. As a key finding, we reveal the
existence of an exotic even-frequency triplet pairing between equal-spin
electrons from different valleys, which arises whenever the spin orientations
in the two valleys are noncollinear. All types of superconducting order turn
out to be highly tunable via straightforward manipulation of the external
exchange field.
