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Operads 2009
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Loday, Jean-Louis and Vallette, Bruno, eds
Séminaires et Congrès 26 (2013), 281 pages
Presentation, Summary

Identities among relations for higher-dimensional rewriting systems
Yves Guiraud, Philippe Malbos
Séminaires et Congrès 26 (2013), 145-161

Résumé :
Identités entre les relations pour la réécriture en dimension supérieure
Nous généralisons la notion d'identités entre les relations, bien connue pour les présentations de groupes, aux présentations de n-catégories par polygraphes. À chaque polygraphe, nous associons une track n-catégorie, généralisant la notion de module croisé pour les groupes, afin de définir son système naturel des identités entre les relations. Nous relions le fait que ce système naturel soit de type fini avec le fait que le polygraphe soit de type de dérivation fini.

Mots-clefs : n-catégorie, réécriture, polygraphe, identités entre les relations, type de dérivation fini.

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.

Keywords: n-category, rewriting, polygraph, identities among relations, finite derivation type.

Class. math. : 18C10, 18D05, 55U99, 68Q42.

ISBN : 978-2-85629-363-8
ISSN : 1285-2783

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