Deino, I think the carrier version, at least at this point, is a pipe dream.
I do not believe the initial design was set up for, or done with carrier operations in mind. Oh, they could alter it and make a version for it. But I do not believe they will even go there until well after the J-20 is operational itself with the PLAAF.
Probably they will want the PLAN to first get its own carrier air wings of J-15s developed and deployed before taking on an entirely new aircraft like that.
But, as with all else...time will tell.
Indeed, it would not make much sense for CAC to start work on a carrier version of the J20 before they get the air force version ready.
However, I think work on it could start sooner than most would expect.
True enough, CAC will need to wait until they get feedback from operational units to see if any adjustments and/or modifications need/could be made to the design to make it better, but unless someone really screwed up somewhere, there shouldn't be any major issues, so this will largely be a case of minor (comparatively) tweaks and adjustments.
However, it will probably take a fair amount of time for any operational unit to convert to the J20 and clock enough hours to start noticing things that could be modified/improved.
That is likely to take a year or more at the earliest, so in the meantime, it would actually make sense to keep the J20 design team together and have them start work on a carrier version.
This way, you can keep the design team largely together, and because they are working on a variant of the plane they designed, all the hard won knowledge and experience they would have gained from the original J20 design would aid them in the new project immeasurably.
Because they are working on a variant, the knew knowledge and experience should not start to erode and over-write the memories and "feel" of the original, so that when the first operational units come back with feedback and design modification requests, they design team would still have all of the J20's knowledge fresh in their minds, even if it has been a year or two since design work finished on the J20.
That in turn, would help speed up any tweaks and changes requested by the air force, and indeed, the two projects could feed into each other, with new innovations thought of during the designing of the carrier version being fed back into the air force version, and useful suggestions for changes by the air force incorporated into the carrier version's design at an early stage.
But even with all of that, I would not really expect to see a carrier version of the J20 until mid to late 2020s, which should, put it on track for the second generation of Chinese carriers, which should be CATOBAR at the minimum, and would likely be considerably larger than the Liaoning design, since it would have been designed from the start with heavy fighters like the J15 and J20 in mind.