  Based on reliable $ab\:initio$ computations and the numerical renormalization
group method, systematic studies on a two-dimensional GaSe monolayer with a Co
adatom have been carried out. It is shown that the stable lowest-energy
configuration of the system involves the Co adatom located over Ga atom. For
such configuration, it is demonstrated that the electronic and magnetic
properties of the system can be effectively controlled by means of external
factors, such as magnetic field, gate voltage or temperature. Moreover, if
properly tuned, the GaSe-Co system can also exhibit the Kondo effect. The
development of the Kondo phenomenon is revealed in the local density of states
of the Co adatom, its magnetic field dependence, which presents the splitting
of the Kondo peak, as well as in the temperature dependence of the conductance,
which exhibits scaling typical of the spin one-half Kondo effect.
