Identities among relations for higher-dimensional rewriting systems

Details Identities among relations for higher-dimensional rewriting systems Identities among relations for higher-dimensional rewriting systems

2009-10-23

arxiv.org/abs/0910.4538v2

Soci\'et\'e Math\'ematique de France, S\'eminaires et Congr\`es 26:145-161 (2011)

Mathematics

Category Theory

16 pages, corrected version after review, to appear in S\'eminaires et Congr\`es

Scientific paper

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

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