An algorithmic approach to Dold-Puppe complexes

Abstract

A Dold-Puppe complex is the image NF\Gamma(C.) of a chain complex C. under the composition of the functors \Gamma, F and N where \Gamma 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 \Gamma(C.). The second half gives an algorithm that allows the explicit calculation of the Dold-Puppe complex NF\Gamma(C.) in terms of the cross-effect functors of F.