Identities among relations for higher-dimensional rewriting systems

Yves Guiraud (1) , Philippe Malbos (2)

1 PAREO - Formal islands: foundations and applications
2 ICJ - Institut Camille Jordan

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.

Domaines: Catégories et ensembles [math.CT]; K-théorie et homologie [math.KT]; Topologie algébrique [math.AT]

Yves Guiraud, Philippe Malbos. Identities among relations for higher-dimensional rewriting systems. 2009. ⟨hal-00426228v1⟩