  The monoidal category of twisted modules of a Vertex Operator Algebra $V$ is
defined and reduced to its 2-group of invertible objects $G_\alpha$, which can
be described by a 3-cocycle $\alpha$ on its 0-truncation $G$ with values in the
group of units $A$ of the field of definition of $V$ serving as its associator.
This cocycle also presents the classifying morphism of an $\infty$-group
extension of $G$ by the delooping $BA$. Motivated by this, it is proven that
the $\infty$-group extension classified by a 3-cocycle $\alpha$ is presented by
the skeletal 2-group $G_\alpha$ with associator $\alpha$. The results are
discussed in light of current developments in Moonshine and $(\infty,1)$-topos
theory.
