The fedora is a wide brimmed cloth hat.
It is a member of the ass hat family of hats which include the fedora, trilby, and cheese-cutter/golf cap.
The fedora is the pinnacle of ass-hattery. The absolute go-to if you want to prove your ass-hattedness, or you believe
your cool factor will avoid an accusation of
being an ass hat.
The Trilby is considered a gateway ass hat. Most ass hats go no further than the trilby.
The cheese-cutter (newsboy/golf cap) is the most forgiving ass hat. It can be worn by many without
immediately appearing an obvious ass hat. It can even be worn backwards. However, this practice was largely discredited in the late 90's.