https://chinapower.csis.org/china-chengdu-j-20/
This will handle Air combat quite fine.
"The short-range PL-10, which was introduced in 2015, is regarded by military analysts as comparable in performance to Western equivalents, such as the Sidewinder II. This year, the PL-15, a radar-guided “beyond visual range” missile (BVRAAM), should enter service. Carried by a J-20, the PL-15 can destroy an aircraft 50km away that is trying to evade it. “The Military Balance” believes that a version of the missile is in the works that will have a cruise speed of Mach 3. It is similar in design to the European Meteor, the best BVRAAM in the West’s inventory, which is only just entering service."
As you say J-20 will be used to deter aircraft carriers and warships.
"A 2015 RAND report noted the J-20’s “combination of forward stealth and long range could hold U.S. Navy surface assets at risk, and that a long-range maritime strike capability may be a cause for greater concern than a short-range air-superiority fighter like the F-22.” The J-20’s size and weapons configuration may, however, preclude it from functioning as an effective strike fighter in either context. Importantly, the mission types Chinese pilots are trained for may determine how the J-20 is eventually utilized."
"The U.S. Naval War College suggests that the J-20 could be an “effective surface-attack platform for out to several hundred nautical miles at sea.” Air Power Australia notes that the J-20 would be a suitable choice of aircraft for operating within China’s “first island chain” and “second island chain.” Should China integrate aerial refueling aircraft with the J-20, the stealth fighter’s operational range would extend even further across the Asia-Pacific."