Geodesic
Higher-dimensional categories with finite derivation type
Theory and applications of categories, Tome 22 (2009), pp. 420-478 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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, generalising the one introduced by Squier for word rewriting systems. We characterise 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.

Classification : 18C10, 18D05, 18D10, 57M20, 68Q42
Keywords: n-category, rewriting, polygraph, finite derivation type, low-dimensional topology 
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     author = {Yves Guiraud and Philippe Malbos},
     title = {Higher-dimensional categories with finite derivation type},
     journal = {Theory and applications of categories},
     pages = {420--478},
     year = {2009},
     volume = {22},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a17/}
}
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Yves Guiraud; Philippe Malbos. Higher-dimensional categories with finite derivation type. Theory and applications of categories, Tome 22 (2009), pp. 420-478. http://geodesic.mathdoc.fr/item/TAC_2009_22_a17/