Ajax was the Captain of the Icarus.
History
Present during the Crisis Meeting, Ajax showed his disbelief of the reports of the Machine army saying that no one has ever seen Sentinels in that big of a group.
He was later killed when his ship was destroyed during the failed EMP counterattack.
Name
His name derives from the son of Telamon, ruler of Salamis and a hero in the Trojan War, also known as "Ajax the Great". Although it would be fitting in the Matrix universe, his name could not have derived from "Asynchronous JavaScript and XML", a technique used in web application development, as this name for the technique was not coined until 2005, after the character first appeared.