There are at least two levels of what an electrical engineer would call a carrier.

1) The IR light itself has a frequency, so technically everything else is modulated onto that carrier frequency. But when you talk about IR signals, you don't call that a carrier nor modulated.

2) Most IR protocols are modulated on a carrier frequency around 38Khz (including as high as the 56Khz Jim mentioned). That modulation means that while the signal is nominally "ON" it is actually switching on and off in a square wave (not a sine wave) at the carrier frequency. Typically that "square" wave isn't actually square; It has a duty cycle around 33% rather than 50%.

Some IR protocols don't have that modulation at all. Rather few, but not as few as the fraction of a percent mentioned above. Fewer are modulated with carrier frequencies far above 56Khz than are unmodulated.