The case or scabbard specifically designed to hold and protect a katana sword is called a "saya." The saya is an integral part of the katana's overall design and functionality. It is typically made of wood and is crafted to precisely fit the shape and dimensions of the sword blade.

The saya serves multiple purposes:

1. Blade Protection: The primary function of the saya is to protect the sharp blade of the katana from damage and to prevent accidental cuts or injuries. The wooden construction helps to shield the blade and keep it secure when not in use.
2. Transportation and Storage: The saya provides a safe and convenient means of transporting and storing the katana. It allows the sword to be carried safely and discreetly, ensuring that the blade is kept covered and the surrounding environment is protected.
3. Aesthetics: The saya is often designed with decorative elements that complement the overall appearance of the katana. It can be adorned with various finishes, lacquers, patterns, or even intricate hand-painted designs to enhance the aesthetic appeal of the sword.

The saya typically features a kurikata (knob) and a sageo (cord). The kurikata is a small knob or loop attached to the saya, which allows for the attachment of a sageo. The sageo is a woven cord that is tied around the saya, providing additional security and facilitating the wearing or carrying of the katana.

It's important to note that the saya is specific to the katana and its related sword types within Japanese sword culture. Other types of swords may have different names for their respective scabbards or cases in their respective cultures.