Yes, a katana is traditionally designed and intended to be sharp. The sharpness of the blade is an essential characteristic of a functional katana. A well-crafted katana has a keen edge that allows it to cut effectively.

In traditional Japanese swordsmithing, great care and attention to detail are given to forging and shaping the katana's blade. The edge is carefully sharpened to achieve a fine cutting edge while maintaining the blade's overall strength and durability.

The cutting ability of a katana relies on its sharpness, as it is primarily designed as a cutting weapon. The curved blade, combined with the sharp edge, allows for efficient and precise slicing and slashing motions. It is worth noting that the katana's design and cutting technique make it most effective when combined with proper training and skill in the hands of a proficient swordsman.

In modern times, while many katana replicas or decorative swords may not have a functional edge, traditional practitioners, martial artists, and collectors often seek out sharp and properly crafted katana blades for their practical use or historical authenticity.

It's important to handle a sharp katana with caution and adhere to proper safety practices when practicing or displaying the sword to prevent accidental injury.