It is possible for a longsword to break a katana, but it would depend on various factors such as the quality of the swords, their construction, and the specific circumstances of the encounter.

Both the longsword and the katana are formidable weapons with their own strengths and weaknesses. The longsword, typically associated with European medieval and Renaissance periods, is a versatile two-handed sword known for its cutting, thrusting, and grappling techniques. The katana, a traditional Japanese sword, is renowned for its sharpness, cutting ability, and speed.

The ability of one sword to break another would primarily depend on factors such as the hardness and durability of the blades, the technique and force applied by the wielder, and the target area being struck.

While the katana's traditional construction involves folding and differential hardening techniques, which can create a durable and resilient blade, it is not invulnerable to damage or breakage. Similarly, the longsword, made of high-quality steel, can be robust and capable of delivering powerful strikes that could potentially damage or break the katana.

In historical encounters, clashes between swords could result in blade damage, breakage, or deformation. Sword fights could lead to various outcomes, including blade-to-blade contact resulting in chips, notches, or breaks, especially if the swords are subjected to significant force or mishandling.

It's worth noting that swords, regardless of type, are designed to withstand the forces encountered in combat to a certain extent, but they are not indestructible. The outcome of a sword-to-sword encounter would depend on the skill, technique, and force applied by the wielders, as well as the quality and construction of the swords involved.

If you have an interest in the art of swordsmanship or martial arts involving different swords, it is recommended to seek proper training from qualified instructors who can teach you the appropriate techniques, safety protocols, and the strengths and limitations of each weapon.

Always prioritize safety and follow the laws and regulations of your jurisdiction when considering the use of any weapon.