Perturbative renormalization in local quantum field theory is described mathematically by the Connes-Kreimer Hopf algebra of Feynman diagrams. This algebra generalizes from usual graphs to ``strand graphs'', the combinatorial objects underlying a broad class of non-local theories, in particular tensorial field theory. As a consequence one can identify Hochschild 1-cocycles and describe the non-perturbative regime of such theories in terms of combinatorial Dyson-Schwinger equations.