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arXiv · 2607.14060

Homotopy of representations up to homotopy

Olivier Brahic·Pedro Frejlich
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Abstract

We propose a general definition of morphism of representations up to homotopy of Lie algebroids, which is be mandated by the requirement that taking cohomology with coefficients in a representation up to homotopy behave functorially. With this definition in place, we show that such representations behave in a similar way to honest representations as far as homotopy invariance of cohomology and local triviality of smooth families are concerned, and for essentially the same reasons as in the classical case.

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Olivier Brahic, Pedro Frejlich. 2026-07-15. Homotopy of representations up to homotopy. https://arxiv.org/abs/2607.14060

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