nLab
free simplicial abelian group

Definition

The free simplicial abelian group functor

Z[]:sSetsAb\mathbf{Z}[-]\colon sSet \to sAb

is given by the functor

sSet=Fun(Δ op,Set)Fun(Δ op,Ab)=sAb,sSet = Fun(\Delta^{op}, Set) \to Fun(\Delta^{op}, Ab) = sAb,

where the middle functor applies the free abelian group functor

Z[]:SetAb.\mathbf{Z}[-]\colon Set \to Ab.

Applications

Free simplicial abelian groups are the crucial ingredient of simplicial chains and simplicial cochains, and such also simplicial homology and simplicial cohomology?, in particular, singular homology and singular cohomology. See these articles for more information.

Created on January 31, 2021 at 19:03:27. See the history of this page for a list of all contributions to it.