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.
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