Homotopy Limits and Homotopy Colimits of Chain Complexes
Algebraic Topology
2026-03-30 v3 Category Theory
Abstract
We give a formula for homotopy limits and homotopy colimits of diagrams of chain complexes using the cobar and bar constructions, also known as the Bousfield--Kan formula. Along the way, we show that the Bousfield--Kan formula computes homotopy colimits in any framed model category.
Keywords
Cite
@article{arxiv.2310.00201,
title = {Homotopy Limits and Homotopy Colimits of Chain Complexes},
author = {Kensuke Arakawa},
journal= {arXiv preprint arXiv:2310.00201},
year = {2026}
}
Comments
Fixed typos, improved exposition, and added references. Identical to the journal version except for a few editorial changes