We demonstrate an equivalence of categories between a certain categories of infinite dimensional representations of quantum $\mathrm{sl}_2$ and two parametrised versions of the Temperley-Lieb category of type $B$. This may be used to discuss semi-simplicity. This is joint work with K. Iohara and R. Zhang.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/8209