## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 10, Number 2 (2008), 149-174.

### Adding inverses to diagrams encoding algebraic structures

#### 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

#### Article information

**Source**

Homology Homotopy Appl., Volume 10, Number 2 (2008), 149-174.

**Dates**

First available in Project Euclid: 1 September 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1251811071

**Mathematical Reviews number (MathSciNet)**

MR2475607

**Zentralblatt MATH identifier**

1154.55013

**Subjects**

Primary: 55U10: Simplicial sets and complexes 18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx] 18C10: Theories (e.g. algebraic theories), structure, and semantics [See also 03G30] 55P35: Loop spaces

**Keywords**

Simplicial groups Segal groupoids diagram categories

#### Citation

Bergner, Julia E. Adding inverses to diagrams encoding algebraic structures. Homology Homotopy Appl. 10 (2008), no. 2, 149--174. https://projecteuclid.org/euclid.hha/1251811071

#### See also

- See: Julia E. Bergner. Adding inverses to diagrams II: Invertible homotopy theories are spaces. Homology Homotopy Appl. Volume 10, Number 2 (2008), 175-193.Project Euclid: euclid.hha/1251811072
- See: Julia E. Bergner. Erratum to "Adding inverses to diagrams encoding algebraic structures" and "Adding inverses to diagrams II: Invertible homotopy theories are spaces". Homology Homotopy Appl. Volume 14, Number 1 (2012), 287-291.Project Euclid: euclid.hha/1355321076