Homotopy Limits and Homotopy Colimits of Chain Complexes
arXiv:2310.00201 · doi:10.1016/j.jpaa.2026.108232
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.
Fixed typos, improved exposition, and added references. Identical to the journal version except for a few editorial changes