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# Homology, Homotopy and Applications

## Volume 10 (2008)

### Number 2

### Adding inverses to diagrams encoding algebraic structures

Pages: 149 – 174

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

#### Author

#### Abstract

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

#### Keywords

simplicial groups; Segal groupoids; diagram categories

#### 2010 Mathematics Subject Classification

18B40, 18C10, 55P35, 55U10

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