  Just as knots and links can be algebraically described as certain morphisms
in the category of tangles in 3 dimensions, compact surfaces smoothly embedded
in R^4 can be described as certain 2-morphisms in the 2-category of `2-tangles
in 4 dimensions'. Using the work of Carter, Rieger and Saito, we prove that
this 2-category is the `free semistrict braided monoidal 2-category with duals
on one unframed self-dual object'. By this universal property, any unframed
self-dual object in a braided monoidal 2-category with duals determines an
invariant of 2-tangles in 4 dimensions.
