There are no internal tags on the one I bought for my son other than the size tag on the collar. The reverse of the size tag shows you can wash at 40 degrees (c), which covers just about every fabric known to man.
By feel, the body and sleeves are definitely wool, but I suspect, because of its designed slim fit and the way the fabric "returns" to shape after being stretched that there is poly in there as well. This is just a guess, though.
The only cotton is the exterior patches on the shoulders and the elbows.