  Using the tensor category theory developed by Lepowsky, Zhang and the second
author, we construct a braided tensor category structure with a twist on a
semisimple category of modules for an affine Lie algebra at an admissible
level. We conjecture that this braided tensor category is rigid and thus is a
ribbon category. We also give conjectures on the modularity of this category
and on the equivalence with a suitable quantum group tensor category. In the
special case that the affine Lie algebra is $\widehat{\mathfrak{sl}}_2$, we
prove the rigidity and modularity conjectures.
