Canterbury cap
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The Canterbury cap is a square cloth hat with sharp corners found in the Anglican communion, similar to the Counter-Reformation's biretta, the notable exception being that a Canterbury cap has four ridges, compared to the biretta's three. It is soft and foldable. The Canterbury cap is the medieval birettum, descended from the ancient pileus headcovering. It is sometimes called the "catercap.". It is also worn today by some women undergraduates at Oxford University instead of the mortarboard.
In the Anglican Church, clergy are entitled to wear the cap. Priests and deacons wear a black version of the headgear; bishops purple.