is kratos a chaos god?

kratos always been affiliated with war nd apocalypse, that’s what he’s the god of, even what the omega symbol means, but also with chaos, zeus stated that kratos was bringing chaos in gow 3, and he put the greek world into chaos single handedly, and it slowly destroyed, and gods, are the god of their professions, it’s one thing to be given godhood, but whatever a god’s talent is, is what they’re the god of, and they control that talent to a universal level, kratos is known to end worlds, put them in chaos, so wouldn’t he be a god of chaos?