Homology, Homotopy and Applications

An algorithmic approach to Dold-Puppe complexes

Ramesh Satkurunath and Bernhard Köck

Full-text: Open access

Abstract

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.

Article information

Source
Homology Homotopy Appl., Volume 12, Number 1 (2010), 301-326.

Dates
First available in Project Euclid: 28 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296223831

Mathematical Reviews number (MathSciNet)
MR2638875

Zentralblatt MATH identifier
1195.13018

Subjects
Primary: 13D25 18G10: Resolutions; derived functors [See also 13D02, 16E05, 18E25] 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10]

Keywords
Dold-Puppe complex simplicial module cross-effect functor

Citation

Satkurunath, Ramesh; Köck, Bernhard. An algorithmic approach to Dold-Puppe complexes. Homology Homotopy Appl. 12 (2010), no. 1, 301--326. https://projecteuclid.org/euclid.hha/1296223831


Export citation