Polygraphic resolutions and homology of monoids (Q1008743)

The second author [\textit{F. Métayer}, ``Resolutions by polygraphs'', Theory Appl. Categ. 11, 148--184 (2003; Zbl 1020.18001)] defined homology using resolutions of \(\omega \)-categories via computads (polygraphs). The classical homology of a monoid \(M\) is defined in terms of resolutions of \(\mathbb{Z}\) by free \(\mathbb ZM\)-modules. The first author showed that the homologies coincide in the case where \(M\) is a group while the present paper proves the coincidence for a general monoid. An unfolding construction and path \(\omega \)-category are involved.