ecclesiastical hat

A red, broad-brimmed hat is chief among the cardinal's insignia; it was granted to secular cardinals by Pope Innocent IV, 1245, and to cardinals belonging to religious orders by Gregory XIV, 1591. It is bestowed on the newly-appointed cardinal at a public consistory, and is not commonly worn; in the absence of the cardinal, and sometimes after his death, it is hung from the roof of the cathedral church. The insignia of a bishop and priest in heraldry include respectively a green and a black hat, of the same shape as the cardinal's, but they have no existence as articles of apparel.
[priest's hat as later developed] [cardinal's hat] [priest's hat as originally allowed]
New Catholic Dictionary

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