Groupoids and the algebra of rewriting in group presentations

Abstract

Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a $2$--complex -- the Squier complex -- whose fundamental groupoid then describes the derivation of consequences of the rewrite rules. We describe a reduced form of the Squier complex, investigate the structure of its fundamental groupoid, and show that key properties of the presentation are still encoded in the reduced form.

arXiv comment15 pages

References in corpus (1)

• Possible connections between whiskered categories and groupoids, many object Leibniz algebras, automorphism structures and local-to-global questions

Cited by in corpus (1)

• The algebra of rewriting for presentations of inverse monoids