  Monolayer transition metal dichalcogenides (TMDs) host deeply bound excitons
interacting with itinerant electrons, and as such they represent an exciting
new quantum many-body Bose-Fermi mixture. Here, we demonstrate that electrons
interacting with a Bose-Einstein condensate (BEC) of exciton-polaritons can
realise a two-dimensional topological $p_x+ip_y$ superconductor. Using strong
coupling Eliashberg theory, we show that this is caused by an attractive
interaction mediated by the BEC, which overcompensates the repulsive Coulomb
interaction between the electrons. The hybrid light-matter nature of the BEC is
crucial for achieving this, since it can be used to reduce retardation effects
and increase the mediated interaction in regimes important for pairing. We
finally show how the great flexibility of TMDs allows one to tune the critical
temperature of the topological superconducting phase to be within experimental
reach.
