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arXiv · 2610.32507

Higher Čech derived functors via Galois theory

Florent Afsa·Tim Van der Linden
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Abstract

We explore sufficient conditions for the higher Čech derived functors of a Birkhoff reflector to agree with its ordinary, Barr-Beck comonadic homology. Using categorical Galois theory together with a spectral-sequence argument, we prove that this is the case for the reflector from any semi-abelian variety onto a subvariety: for every $n\geq 1$, the $n$th Čech derived functor of the reflector coincides with its $(n+1)$st comonadic homology object. More generally, the comparison holds for any Birkhoff reflector of a semi-abelian category equipped with a comonad satisfying Quillen's conditions.

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Florent Afsa, Tim Van der Linden. 2026-10-23. Higher Čech derived functors via Galois theory. https://arxiv.org/abs/2610.32507

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