Teisi in $\underline{\rm Ab}$

Abstract

Teisi are certain higher-dimensional categorical structures proposed for doing non-abelian homotopical and homological algebra. I give a partial justification for this proposal by showing that in the abelian case teisi indeed reduce to chain complexes. I also show that the result holds for a much wider class of weaker higher-dimensional categorical structures, which however need to have strict identities. The main step in the proof is an elegant Eckmann-Hilton type argument.