Homology, Homotopy and Applications
Volume 12 (2010)
An algorithmic approach to Dold-Puppe complexes
Pages: 301 – 326
A Dold-Puppe complex is the image $NFΓ(C.)$ of a chain complex $C$. under the composition of the functors $Γ$, $F$ and $N$, where $Γ$ and $N$ are given by the Dold-Kan correspondence and $F$ is a not necessarily linear functor between two abelian categories. The first half of this paper gives an algorithm that streamlines the calculation of $Γ(C.)$. The second half gives an algorithm that allows the explicit calculation of the Dold-Puppe complex $NFΓ(C.)$ in terms of the cross-effect functors of $F$.
Dold-Puppe complex; simplicial module; cross-effect functor
2010 Mathematics Subject Classification