The scabbard of a katana is called a "saya." The saya is a protective sheath that encases the blade when it is not in use. It is typically made of wood and is designed to fit the specific shape and dimensions of the katana.

The saya is an essential component of the katana and serves several purposes. It protects the blade from damage and corrosion, prevents accidents or injury when handling the sword, and allows for safe storage and transportation.

The saya is often lacquered or coated with various finishes to enhance its durability and aesthetic appearance. It can be decorated with elaborate designs, inlays, or fittings, depending on the style, period, and personal preferences.

Additionally, the saya usually includes other fittings such as the koiguchi (mouth of the scabbard), kurikata (knob or cord holder), and the sageo (the cord used to secure the saya to the obi or belt).

Overall, the saya is an integral part of the katana, complementing the blade and handle to create a functional and visually appealing weapon.