An algorithmic approach to Dold-Puppe complexes

TL;DR

This paper introduces algorithms to efficiently compute Dold-Puppe complexes, especially focusing on calculating the complex NFΓ(C.) using the Dold-Kan correspondence and cross-effect functors.

Contribution

It provides the first algorithmic method for explicitly calculating Dold-Puppe complexes in terms of cross-effect functors of F.

Findings

Streamlined algorithm for calculating Γ(C.)

Explicit calculation method for NFΓ(C.)

Application of cross-effect functors in complex computation

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.