Ribbon categories of weight modules for affine $\mathfrak{sl}_2$ at admissible levels

We show that the braided tensor category of finitely-generated weight modules for the simple affine vertex operator algebra $L_k(\mathfrak{sl}_2)$ of $\mathfrak{sl}_2$ at any admissible level $k$ is rigid and hence a braided ribbon category. The proof uses a recent result of the first two authors wi