  Murray, Roberts and Wockel showed that there is no strict model of the string
2-group using the free loop group. Instead, they construct the next best thing,
a coherent model for the string 2-group using the free loop group, with
explicit formulas for all structure. Based on their expectations, we build a
category of 2-representations for coherent Lie 2-groups and some concrete
examples. We also discuss the relation between this category of
2-representations and the category of representations. In addition, we
construct a model of equivariant 2-vector bundles. At the end, we discuss the
adjoint action on the string 2-representations.
