Cagney is Elisa Maza's pet cat.
Greg Weisman has said that Cagney wasn't adopted at a shelter by Elisa, but rather Cagney adopted Elisa, hinting that Cagney may have been a stray cat. In late 1996, Cagney was about three years old.
Cagney is, fortunately, good at looking after himself when Elisa is absent. When Elisa disappeared during the Avalon World Tour, Brooklyn, Broadway, and Lexington and Hudson took Cagney back to the clock tower, where he and Hudson developed a friendship.  Cagney approved of Jason Conover, when he briefly stopped by at Elisa's apartment.