Generalized action monads and descent
Category Theory
2026-07-10 v1
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.
Cite
@article{arxiv.2607.09595,
title = {Generalized action monads and descent},
author = {Elena Caviglia and Sophie Marques and Luca Mesiti},
journal= {arXiv preprint arXiv:2607.09595},
year = {2026}
}