The Galero.

The cast of Der Tiefstapler - 1978 includes: Alejandro de Enciso as Galero Ricardo Merino as Finanzminister Ricardo Palacios as Verkehrsminister Nava Ruano as Ginda Georg Thomalla as Christian Sturm Adolfo Thous

A cardinal's galero (up until the Second Vatican Council, they are not longer required) is hung over a Cardinal's tomb and left there until it turns to dust - symbolizing the end of all earthly things. No, they are never removed, they are left until time takes them.

The tall hat used by bishops of the Latin rite during the celebration of the Mass and certain other ceremonies is called a "miter." There are other types of headcoverings as well, like the galero, saturno, and zucchetto.

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.