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arXiv · 2310.00201

Homotopy Limits and Homotopy Colimits of Chain Complexes

Kensuke Arakawa
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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.

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Kensuke Arakawa. 2023-09-30. Homotopy Limits and Homotopy Colimits of Chain Complexes. https://doi.org/10.1016/j.jpaa.2026.108232

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