Higher-dimensional categories with finite derivation type

Details Higher-dimensional categories with finite derivation type Higher-dimensional categories with finite derivation type

2008-10-08

arxiv.org/abs/0810.1442v2

Theory and Applications of Categories 22(18):420-478 (2009)

Mathematics

Category Theory

Scientific paper

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.

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