Some quantum phases of matter are described different patterns of quantum entanglement. The patterns of quantum entanglement are new phenomena that happen in nature. But what kind of mathematical language do we use to describe quantum entanglement. Here I would like to explain that fusion category theory and group cohomology theory are nature languages to describe various patterns of quantum entanglement. As a result, we can use fusion category theory and group cohomology theory to classify new quantum states of matter.