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arXiv · 2607.09595

Generalized action monads and descent

Elena Caviglia·Sophie Marques·Luca Mesiti
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Abstract

We develop a monadic approach to actions of internal categories. Given an internal category, we construct a monad on a slice whose algebras are the actions of that internal category. Then, we give a complete characterization of the monads that arise in this way; we call them generalized action monads. Finally, we prove that these monads yield a well-behaved notion of generalized descent.

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Elena Caviglia, Sophie Marques, Luca Mesiti. 2026-07-10. Generalized action monads and descent. https://arxiv.org/abs/2607.09595

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