# Simplicial group

In mathematics, more precisely, in the theory of simplicial sets, a **simplicial group** is a simplicial object in the category of groups. Similarly, a **simplicial abelian group** is a simplicial object in the category of abelian groups. A simplicial group is a Kan complex (in particular, its homotopy groups make sense.) The Dold–Kan correspondence says that a simplicial abelian group may be identified with a chain complex.

A commutative monoid in the category of simplicial abelian groups is a simplicial commutative ring.

## References

- Goerss, P. G.; Jardine, J. F. (1999).
*Simplicial Homotopy Theory*. Progress in Mathematics.**174**. Basel, Boston, Berlin: Birkhäuser. ISBN 978-3-7643-6064-1. - Charles Weibel,
*An introduction to homological algebra*

## External links

- simplicial group in
*nLab* - http://mathoverflow.net/questions/118500/what-is-a-simplicial-commutative-ring-from-the-point-of-view-of-homotopy-theory/

This article is issued from Wikipedia - version of the 10/13/2013. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.