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/
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