The B\'enabou-Roubaud theorem via string diagrams
Category Theory
2026-01-13 v2
Abstract
We give a complete proof of the B\'enabou-Roubaud monadic descent theorem using the graphical calculus of string diagrams. Our proof links the monadic and Grothendieck's original viewpoint on descent via an internal-category-based characterization of the category of descent data, equivalent to the one of Janelidze and Tholen.
Cite
@article{arxiv.2601.05691,
title = {The B\'enabou-Roubaud theorem via string diagrams},
author = {Jovana Obradović},
journal= {arXiv preprint arXiv:2601.05691},
year = {2026}
}
Comments
This article provides a formal and self-contained account of the authors unpublished 2016 note