  The diagrammatic coaction encodes the analytic structure of Feynman integrals
by mapping any given Feynman diagram into a tensor product of diagrams defined
by contractions and cuts of the original diagram. Feynman integrals evaluate to
generalized hypergeometric functions in dimensional regularization.
Establishing the coaction on this type of functions has helped formulating and
checking the diagrammatic coaction of certain two-loop integrals. In this talk
we study its application on the fully massless double box diagram. We make use
of differential equation techniques, which, together with the properties of
homology and cohomology theory of the resulting hypergeometric functions, allow
us to formulate the coaction on a range of cuts of the double box in closed
form.
