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Higher-dimensional categories with finite derivation type

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Yves Guiraud and Philippe Malbos

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.

Keywords:
n-category, rewriting, polygraph, finite derivation type, low-dimensional
topology

2000 MSC:
18C10, 18D05, 18D10, 57M20, 68Q42

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 18, pp 420-478.

http://www.tac.mta.ca/tac/volumes/22/18/22-18.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/18/22-18.pdf

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