On the derived functors of destabilization and of iterated loop functors

TL;DR

This paper develops a method to construct small functorial chain complexes that compute derived functors related to destabilization and iterated loop functors in the context of modules over the mod 2 Steenrod algebra, unifying previous results.

Contribution

It introduces a unified approach to calculating derived functors of destabilization and iterated loop functors using small functorial chain complexes, connecting Singer and Lannes-Zarati results.

Findings

Constructed small functorial chain complexes for derived functors

Unified results of Singer and Lannes-Zarati

Enhanced computational tools for Steenrod algebra modules

Abstract

These notes explain how to construct small functorial chain complexes which calculate the derived functors of destabilization (respectively iterated loop functors) in the theory of modules over the mod 2 Steenrod algebra; this shows how to unify results of Singer and of Lannes and Zarati.