Here's more on ecclesiastical headgear, again from Wikipedia via answers.com:
A cappello romano (literally Roman hat) is a hat with a wide, circular brim and a rounded rim worn by Catholic clergy. It is made of either beaver fur or felt, and lined in white silk. Unlike many other articles of ecclesiastical attire, it serves no ceremonial purpose, being primarily a practical item. (The galero is a ceremonial wide brim hat no longer worn.) The wearing of a cappello romano is optional, but it is never worn during services. It is generally uncommon outside of Rome today.
There are some, mostly minor, differences in the designs of cappelli, depending on the rank of the wearer. The pope wears a red cappello with gold cords. All other clerics wear black cappelli. A cardinal may have a cappello with red and gold cords with scarlet lining. A bishop's may have green and gold cords with violet lining. A priest may substitute black lining for his. Cappelli worn by deacons and seminarians have no distinguishing items.
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