  We theoretically investigate the emission properties of a single-mode cavity
coupled to a mesoscopic number of incoherently pumped quantum emitters. We
propose an operational measure for the medium cooperativity, valid both in the
bad and in the good cavity regimes. We show that the opposite regimes of
subradiance and superradiance correspond to negative and positive
cooperativity, respectively. The lasing regime is shown to be characterized by
nonnegative cooperativity. In the bad cavity regime we show that the
cooperativity defines the transitions from subradiance to superradiance. In the
good cavity regime it helps to define the lasing threshold, also providing
distinguishable signatures indicating the lasing regime. Increasing the quality
of the cavity mode induces a crossover from the solely superradiant to the
lasing regime. Furthermore, we verify that lasing is manifested in a wide range
of positive cooperative behavior, showing that stimulated emission and
superradiance can coexist. The robustness of the cooperativity is studied with
respect to experimental imperfections, such as inhomogeneous broadening and
pure dephasing.
