Higher-dimensional categories with finite derivation type
Identifieur interne : 003767 ( Main/Exploration ); précédent : 003766; suivant : 003768Higher-dimensional categories with finite derivation type
Auteurs : Yves Guiraud [France] ; Philippe Malbos [France]Source :
- Theory and Applications of Categories [ 1201-561X ] ; 2009.
English descriptors
Abstract
We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalizing the one introduced by Squier for word rewriting systems. We characterize this property by using the notion of critical branching. In particular, we define sufficient conditions for an n-category to have finite derivation type. Through examples, we present several techniques based on derivations of 2-categories to study convergent presentations by 3-polygraphs.
Url:
Affiliations:
- France
- Auvergne-Rhône-Alpes, Grand Est, Lorraine (région), Rhône-Alpes
- Lyon, Nancy, Saint-Étienne
- Institut national polytechnique de Lorraine, Université Claude Bernard Lyon 1, Université Jean Monnet Saint-Etienne, Université Nancy 2, Université de Lorraine, Université de Lyon
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Le document en format XML
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Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalizing the one introduced by Squier for word rewriting systems. We characterize this property by using the notion of critical branching. In particular, we define sufficient conditions for an n-category to have finite derivation type. Through examples, we present several techniques based on derivations of 2-categories to study convergent presentations by 3-polygraphs.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Auvergne-Rhône-Alpes</li><li>Grand Est</li><li>Lorraine (région)</li><li>Rhône-Alpes</li></region><settlement><li>Lyon</li><li>Nancy</li><li>Saint-Étienne</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Claude Bernard Lyon 1</li><li>Université Jean Monnet Saint-Etienne</li><li>Université Nancy 2</li><li>Université de Lorraine</li><li>Université de Lyon</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Guiraud, Yves" sort="Guiraud, Yves" uniqKey="Guiraud Y" first="Yves" last="Guiraud">Yves Guiraud</name></region><name sortKey="Malbos, Philippe" sort="Malbos, Philippe" uniqKey="Malbos P" first="Philippe" last="Malbos">Philippe Malbos</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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