Spectral Sequences in Semi-Abelian Categories

Abstract

In this paper, we define the notion of a spectral sequence in the context of semi-abelian categories in the sense of Janelidze, Márki and Tholen. We show that from a double simplicial object, one can construct an exact couple, which gives rise to a spectral sequence. This extends Quillen's result on double simplicial groups to every semi-abelian category.