Higher-dimensional categories with finite derivation type
Yves Guiraud, Philippe Malbos · Theory and applications of categories · 2009
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.Contents 1 Higher-dimensional categories presented by polygraphs 426 2 Contexts, modules and derivations of n-categories 431 3 Higher-dimensional categories with finite derivation type 437 4 Critical branchings and finite derivation type 442 5 The case of 3-polygraphs 449This work has been partially supported by ANR INVAL project (ANR-05-BLAN-0267).