$\operatorname{Rep}(H)$ and the double

For a semisimple $H$, rep_category(H) computes numerically, at any precision:

• central primitive idempotents and matrix blocks, so the irreducible representations;
• tensor products through $\Delta$, so the fusion rules $N_{ab}^{c}$;
• Clebsch–Gordan maps and the $F$-symbols;
• with an $R$-matrix, the $R$-symbols, and for a modular category $S$ and $T$.

When the unit is not simple, Rep(H) is multifusion and is cut along $1 = \bigoplus_{i} 1_{i}$ into the fusion categories $1_{i} \otimes \operatorname{Rep}(H) \otimes 1_{i}$.

Drinfeld double

drinfeld_double_weak(H) builds $D(H) = (\hat{H}^{\mathrm{op}} \otimes H)/J$ (Nikshych–Vainerman) with its canonical $R$-matrix, exactly, and $\operatorname{Rep} D(H) \simeq \mathcal{Z}(\operatorname{Rep} H)$.