4 problems

Let $G$ be a group. For a multifusion category $\mathcal{C}$ with a $G$-action, write $\mathcal{C}^G$ for its equivariantization and $\mathbf{Mod}(\mathcal{C})$ for its delooping.…

Let $A$ be an abelian group with $A_e\cong\mathbb{Z}_{2^n}\times\mathbb{Z}_2$ for $n\geq2$. Mixed-even-part conjecture. The modular data of the Drinfeld center of the…

Let $A$ be an abelian group with $A_e\cong\mathbb{Z}_{2^{n+1}}$. Cyclic-even-part de-equivariantization conjecture. The modular data of the Drinfeld center of the $\mathbb{Z}_2$-de…

Let $A$ be an odd finite abelian group and let $G=\mathbb{Z}_{2^n}\times A$ with $n\geq1$. Inverse-involution near-group conjecture. The constructed modular data are the modular da…