We construct symmetric monoidal categories LRF,LFG of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf algebras of LRF,LFG, HLRF,HLFG are dual to the corresponding Connes-Kreimer Hopf algebras on rooted trees and Feynman diagrams.We thus obtain an interpretation of the Connes-Kreimer Lie algebras on rooted trees and Feynman graphs as Ringel-Hall Lie algebras.
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