The hydraulic clutch linkage in your vehicle is self-adjusting. This system does not have its own reservoir. It receives fluid from the brake master cylinder reservoir.
See Brakes on for more information.
Chevrolet Cobalt Service & Repair Manual. General Service
Two basic types of power assist
mechanisms are used: vacuum assist diaphragm assemblies, which use engine
vacuum or in some cases vacuum pressure developed by an external vacuum
pump. The second type is a hydraulic pressure assist mechanism, which use
pressure developed by an ...