The F-22 is not carrier based and I doubt it could take off from one. Lockheed Martin proposed a carrier version, but the Navy wasn't biting. The USAF F-22 doesn't have the necessary components for carrier operation - special stuff for the catapult, beefier air frame and arrestor hook for landing. The F-22 is also an air superiority fighter - I doubt it would really be needed to fight NK.
The F22 could take off from a carrier. It needs 800ft and the runway on a carrier is just shy of 1000ft. Landing it could not do because it lacks the landing gear support.
I was curious so I asked some friends who are still active duty, they had 4 on deck Saturday on the way to Okinawa, Japan. , it has been years since I was in the Navy, I went in as an aviation electronics guy in the early 90's. and we transported many planes for the air force on carriers .
I was also reminded by friends that the air force cannot use a navy carrier for any of their planes to take off because it is against the rules. They will help each other but the Navy can't provide functions that would normally be performed by the Air Force. It doesn't matter if it is a model toy plane, if it has the air force logo and the air force usually supervises its setting down, the Navy can't perform that function .They have the whole we are part of the same military, but what is our branch belongs to our branch thing going on.
Navy may take marine soldiers to a fight, but the second the Navy starts trying to drive a tank off a transport, the Marines will throw a fit.
They could be using the carrier to transport them, but I don't see why they'd do that. You'd have to dock somewhere and remove them from the ship to bring them back to active use (since they are not carrier capable). Why not just fly them to a more local airbase if you need them?
It is done quite a lot to transport planes. They are just left on deck since they cannot be stored in the hanger on ship without some serious mechanical reworking. The reason they transport planes vs flying them there is it is easier than doing multiple in air refueling per plane just to get it to a destination.
I thought it was interesting that Japan sent 4 observers . Japan was really against the F-22 being based there but has given into the idea over the past couple years.