Identities among relations for higher-dimensional rewriting systems

Yves Guiraud 1, 2, * Philippe Malbos 3, *
* Corresponding author
1 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : 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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Yves Guiraud, Philippe Malbos. Identities among relations for higher-dimensional rewriting systems. Séminaires et congrès, Société mathématique de France, 2013, 26, pp.145-161. ⟨hal-00426228v2⟩

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