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We generalize the notion of identities among relations, well known forpresentations of groups, to presentations of n-categories by polygraphs. Toeach polygraph, we associate a track n-category, generalizing the notion ofcrossed module for groups, in order to define the natural system of identitiesamong relations. We relate the facts that this natural system is finitelygenerated and that the polygraph has finite derivation type.

Identities among relations for higher-dimensional rewriting systems