  An analog of Kreimer's coproduct from renormalization of Feynman integrals in
quantum field theory, endows an analog of Kontsevich's graph complex with a
dg-coalgebra structure. The graph complex is generated by orientation classes
of labeled directed graphs. A graded commutative product is also defined,
compatible with the coproduct. Moreover, a dg-Hopf algebra is identified.
  Graph cohomology is defined applying the cobar construction to the
dg-coalgebra structure.
  As an application, L-infinity morphisms represented as series over Feynman
graphs correspond to graph cocycles. Notably the total differential of the
cobar construction corresponds to the L-infinity morphism condition. The main
example considered is Kontsevich's formality morphism.
  The relation with perturbative quantum field theory is considered by
interpreting L-infinity morphisms as partition functions, and the coefficients
of the graph expansions as Feynman integrals.
