The Grumman F3F was designed to operate from a carrier. But as far as I know, it did not do so during the war. Most, if not all the F3Fs that saw action, did so from land bases as part of the Chinese Air Force. BUT, if it is included in AH2, I think it should be considered a carrier type.
It might interest you to know that Gen. Chuck Yeager thought the P39 was a really sweet machine. I can't remember the exact quote, but I recall reading his auto-biography somewhere that he preferred it to the P51.