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arXiv · 2601.05691

The B\'enabou-Roubaud theorem via string diagrams

Jovana Obradović
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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.

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Jovana Obradović. 2026-01-09. The B\'enabou-Roubaud theorem via string diagrams. https://arxiv.org/abs/2601.05691

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