PreprintCC BY 4.0arXiv
Higher Čech derived functors via Galois theory
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≥ 1, the nth 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.
Related
- Anomalies, higher symmetries, and homotopy theory I: crossed precosheaves and a nonabelian Cech construction
- Galois and separable extensions of Tambara functors
- The first Cech derived functor
- Derived functors and Hilbert polynomials over dominant Cohen-Macaulay rings
- Equivalence of categories of bivariant K-theory for C*-algebras over topological spaces via reflection functors
BibTeX
@misc{afsa2026higher,
title = {{Higher Čech derived functors via Galois theory}},
author = {Florent Afsa and Tim Van der Linden},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32507},
eprint = {2610.32507},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32507},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Higher Čech derived functors via Galois theory
AU - Florent Afsa
AU - Tim Van der Linden
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32507
UR - https://arxiv.org/abs/2610.32507
AB - 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≥ 1, the nth 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.
ER -