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Higher-dimensional categories with finite derivation type

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 نشر من قبل Yves Guiraud
 تاريخ النشر 2009
  مجال البحث
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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, 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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