cowl
Hood covering the head, worn by the monastic orders.
In the Middle Ages the cloak had a cowl attached which could be drawn over the head, and the cowl became a great cloak with a hood.
The cowl of the Benedictines, Cistercians, etc. is a great mantle with a hood which may be thrown back over the shoulders; the Franciscans have a smaller hood attached to their habit.
Canons wear it on their mozzetta and bishops and cardinals on the cappa; the cowl of the Augustinians and Servites is a separate hood.
The color of the cowl is that of the habit.
New Catholic Dictionary
