  We predict the emergence of a time crystal generated by an incoherently
driven and dissipative nonlinear optical oscillator, where the nonlinearity
also comes from dissipation. We show that a second-order dissipative phase
transition of light occurs in the frame rotating at the cavity frequency, while
a boundary (dissipative) time crystal emerges in the laboratory frame. We
relate these two phenomena by using the Liouvillian superoperator associated
with the Lindblad master equation and its symmetries. These results connect the
emergence of a second-order dissipative phase transition and a dissipative time
crystal in the thermodynamic limit, allowing to interpret them as the same
phenomenon in terms of the Liouvillian spectrum, but just in different frames.
