A mitre

mitre.

The 'beanie" bishops wear for ceremonial occasions in their robes, is called a zucetto, it is purple, the Pope's white one is quite familiar from TV, cardinals crimson.

The hat is called a mitre.

a miter i believe.

It is called a MITRE. According to the Catholic encyclopedia: The mitre is a kind of folding-cap. It consists of two like parts, each stiffened by a lining and rising to a peak; these are sewn together on the sides, but are united above by a piece of material thet can fold together. Two lappets trimmed on the ends with fringe hang down from the back. The mitre is, theoretically, always supposed to be white. The official "Cæremoniale Romanum" distinguishes three kinds of mitres: the mitra pretiosa, auriphrygiata, and simplex. The first two differ from each other only in the greater or less richness of the ornamentation; the mitra simplex, or simple mitre, is one of white silk or white linen entirely without ornament. The fringe on the lappets at the back should be red. The bishop must wear the mitra pretiosa on those days on which the hymn Te Deum is used in the Office, the mitre auriphrygiata in the seasons of Advent and Lent, on fast days and during penitential processions, the mitra simplex on Good Fridays, at funerals, and at the blessing of the candles on Candlemas-day. When bishops attend a general council, or are present at solemn pontifical acts of the pope, they wear a plain linen mitre, while the cardinals on occasions wear a simple mitre of silk damask. The right to wear the mitre belongs by law only to the pope, the cardinals, and the bishops. Others require for its use a special papal privilege. This privilege is possessed, for example, by numerous abbots, the dignitaries of many cathedral chapters, and by certain prelates of the papal Curia, but, as a rule, the right is more or less limited: for instance, such prelates can only use a simple mitre of white linen, unless the contrary is expressly granted them. The mitre is distinguished from the other episcopal vestments in that it is always laid aside when the bishop prays; for example, at the orationes of the Mass, of the Office, in conferring Holy Orders, at the Canon of the Mass, etc. The reason for this is to be found in the commandment of the Apostle that a man should pray with uncovered head (1 Corinthians 11:4). The giving of the mitre is a ceremony in the consecration of a bishop. It occurs at the close of the Mass after the solemn final blessing, the consecrator having first blessed the mitre.

It's called a mitre and it's first placed on the bishop's head during his consecration ceremony.

I think it's called a gallero

I think it may be called a mitre...

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a ceremonial hat of a bishop is i think a mitre

The Bishop's hat is called a Mitre