A Japanese hairstyle; a type of hair ring.
A ponytail is made from the roots of the hair, tied into into a topknot, and then looped, creating a ring against or above the crown of the head.
The hairstyle's name stems from a person - during the early Edo period, Katsuyama was the pseudonym of a high-ranking courtesan popular in Yoshiwara during the early Edo period. Mage translates to 'hairstyle'.