English

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.

Keywords

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This article provides a formal and self-contained account of the authors unpublished 2016 note

R2 v1 2026-07-01T08:57:35.818Z