  A central extension of the loop group of a Lie group is called transgressive,
if it corresponds under transgression to a degree four class in the cohomology
of the classifying space of the Lie group. Transgressive loop group extensions
are those that can be explored by finite-dimensional, higher-categorical
geometry over the Lie group. We show how transgressive central extensions can
be characterized in a loop-group theoretical way, in terms of loop fusion and
thin homotopy equivariance.
