On the B\'enabou-Roubaud theorem
Category Theory
2025-04-18 v2
Abstract
We give a detailed proof of the B\'enabou-Roubaud theorem. As a byproduct it yields a weakening of its hypotheses: the base category does not need fibre products and the Beck-Chevalley condition, in the form of a natural transformation, can be weakened by only requiring the latter to be epi.
Cite
@article{arxiv.2404.00868,
title = {On the B\'enabou-Roubaud theorem},
author = {Bruno Kahn},
journal= {arXiv preprint arXiv:2404.00868},
year = {2025}
}
Comments
Final version, to appear in Cahiers de topologie et g\'eom\'etrie diff\'erentielle cat\'egoriques