*Tensor categories* were introduced as abstract structures to unify properties of tensor products used in algebra, algebraic topology, representation theory, and operator algebra.

Tensor categories which
have an additional structure called *braiding* have found applications in
describing the behavior of particle systems in theoretical physics. This
additional structure connects such categories to the braid group and its
representations.

I will talk about how these ingredients come together
in *topological quantum computing,* which is one of the approaches
proposed to build a quantum computer.