We introduce a categorical framework for the study of representations
of G(F), where G is a reductive group, and F is a 2-dimensional
local field, i.e. F = K((t)), where K is a local field.
Our main result says that the space of functions on G(F), which is an
object of a suitable category of representations of G(F) with the respect to
the action of G on itself by left translations, becomes a representation of
a certain central extension of G(F), when we consider the action by right
translations.