Categorical Tori - Ganter, N. (Symmetry, Integrability and Geometry: Methods and Applications, 2018)
We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal Tori of simple and simply connected compact Lie groups and the Tori associated with the Leech and Niemeyer lattices. We obtain the extra-special 2-groups as the isomorphism classes of categorical fixed points under an involution action.