The Bénabou-Roubaud theorem via string diagrams
Abstract
We give a complete proof of the Bénabou-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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Logic
programming
and type systems
Advanced Algebra and Logic
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 January 2026
- Document type
- Preprint