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Journal Articles Theory and Applications of Categories Year : 2009

Higher-dimensional categories with finite derivation type

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.
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Dates and versions

hal-00326974 , version 1 (06-10-2008)
hal-00326974 , version 2 (20-10-2009)

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Cite

Yves Guiraud, Philippe Malbos. Higher-dimensional categories with finite derivation type. Theory and Applications of Categories, 2009, 22 (18), pp.420-478. ⟨10.48550/arXiv.0810.1442⟩. ⟨hal-00326974v2⟩
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