The DG-category of secondary cohomology operations

Baues, Hans-Joachim; Frankland, Martin

doi:10.1007/s10485-020-09601-1

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The DG-category of secondary cohomology operations

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Baues, Hans-Joachim
Max Planck Institute for Mathematics, Max Planck Society;

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Frankland, Martin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s10485-020-09601-1
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arXiv:1811.08077.pdf
(Preprint), 386KB

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Citation

Baues, H.-J., & Frankland, M. (2020). The DG-category of secondary cohomology operations. Applied Categorical Structures, 28(6), 877-905. doi:10.1007/s10485-020-09601-1.

Cite as: http://hdl.handle.net/21.11116/0000-0006-BC49-5

Abstract

We study track categories (i.e., groupoid-enriched categories) endowed with additive structure similar to that of a 1-truncated DG-category, except that composition is not assumed right linear. We show that if such a track category is right linear up to suitably coherent correction tracks, then it is weakly equivalent to a 1-truncated DG-category. This generalizes work of the first author on the strictification of secondary cohomology operations. As an application, we show that the secondary integral Steenrod algebra is strictifiable.