Higher-dimensional normalisation strategies for acyclicity
In 1994, Squier linked the existence of a finite convergent presentation of a monoid to a homotopical invariant of monoids, called finite derivation type. Using this result, he gave another proof that there exists finitely generated monoids with a decidable word problem that do no admit a finite convergent presentation.NEWLINENEWLINE In this paper, the authors use normalisation strategies to construct an explicit polygraphic resolution from a convergent presentation. They define a higher-dimensional homotopical finiteness condition for higher categories which is an extension of Squier's finite derivation type for monoids, and relate it to a new homological finiteness condition.
scientific article; zbMATH DE number 6094113
scientific article