Boardman's whole-plane obstruction group for Cartan-Eilenberg systems

Abstract

Each extended Cartan--Eilenberg system $(H,\partial )$ gives rise to two exact couples and one spectral sequence. We show that the canonical colim-lim interchange morphism associated to $H$ is a surjection, and that its kernel is isomorphic to Boardman's whole-plane obstruction group $W$, for each of the two exact couples.