  In this article we formulate and prove the main theorems of the theory of
character sheaves on unipotent groups over an algebraically closed field of
characteristic p>0. In particular, we show that every admissible pair for such
a group G gives rise to an L-packet of character sheaves on G, and that,
conversely, every L-packet of character sheaves on G arises from a (non-unique)
admissible pair.
  In the appendices we discuss two abstract category theory patterns related to
the study of character sheaves. The first appendix sketches a theory of duality
for monoidal categories, which generalizes the notion of a rigid monoidal
category and is close in spirit to the Grothendieck-Verdier duality theory. In
the second one we use a topological field theory approach to define the
canonical braided monoidal structure and twist on the equivariant derived
category of constructible sheaves on an algebraic group; moreover, we show that
this category carries an action of the surface operad. The third appendix
proves that the "naive" definition of the equivariant constructible derived
category with respect to a unipotent algebraic group is equivalent to the
"correct" one.
