Spinors
Starting with an orthonormal coordinate system, a tensor transforms in a certain way when a rotation is applied. However, there is additional structure to the group of rotations that is not exhibited by the transformation law for tensors: see orientation entanglement and plate trick. Mathematically, the rotation group is not simply connected. Spinors are mathematical objects that generalize the transformation law for tensors in a way that is sensitive to this fact.
Read more about this topic: Tensor, Generalizations