Homology, Homotopy and Applications

Volume 10 (2008)

Number 2

Adding inverses to diagrams encoding algebraic structures

Pages: 149 – 174

DOI: https://dx.doi.org/10.4310/HHA.2008.v10.n2.a8


Julia E. Bergner (Department of Mathematics, University of California at Riverside)


We modify a previous result, which showed that certain diagrams of spaces are essentially simplicial monoids, to construct diagrams of spaces which model simplicial groups. Furthermore, we show that these diagrams can be generalized to models for Segal groupoids. We then modify Segal’s model for simplicial abelian monoids in such a way that it becomes a model for simplicial abelian groups


simplicial groups, Segal groupoids, diagram categories

2010 Mathematics Subject Classification

18B40, 18C10, 55P35, 55U10

Published 1 January 2008

An erratum to this article is available as HHA 14(1) pp. 287-291.