Higher-dimensional categories with finite derivation type
Category Theory
2009-10-20 v2 Algebraic Topology
K-Theory and Homology
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.
Cite
@article{arxiv.0810.1442,
title = {Higher-dimensional categories with finite derivation type},
author = {Yves Guiraud and Philippe Malbos},
journal= {arXiv preprint arXiv:0810.1442},
year = {2009}
}