The pointed hat that an Archbishop wears during Mass and other sacred ceremonies is called the mitre.
The maroon-colored hat with three fins and a pom-pom on it is called a biretta.
The hood an Archbishop traditionally covers his head with at Tenebrae during Holy Week is the hood of the Cappa Magna.
Miter
It is called a mitre and is also worn by all bishops, archbishops and cardinals. It is symbolic of a bishop. And is also considered a tradition as it dates back to the medieval days.
The box-like caps are called biretta ( singular birettum) Bishops wear purple ones. Cardinals wear red. There is a red brimmed hat the cardinals may wear called a galero. The skullcap worn by bishops, cardinals and the pope is called a zucchetto.
In the Catholic Church, Bishops, Archbishops, and Cardinals wear the pinkish red hats called a biretta (pronounced ba-ret-a). The biretta, a 4 cornered hat, has 3 points which refers to The Trinity. See this biretta.
An Archbishop is just a Bishop of an Archdiocese, so, not counting retired archbishops, there are 33 Archbishops as there are 33 Archdioceses in the United States. Cardinals are mostly Archbishops.
bishops and archbishops
cap and gown. the hat is called a mortarboard.
It is called a Zuchetto and it comes in various colours: White : The Pope and members of the Dominican and Norbetine religious orders Red: Cardinals Violet: (Called Amaranth Red by the RCC) Patriarchs, Archbishops and Bishops Black: Priests and Deacons.
a leperchaun's hat :P
The hat is also called a homburg hat in English.
Its called a hat box
According to Irish folklore, it's called a cocked hat.
A guardsman hat is called 'Bear Skin'