On the Bénabou-Roubaud theorem
arXiv:2404.00868
Abstract
We give a detailed proof of the Bénabou-Roubaud theorem. As a byproduct it yields a weakening of its hypotheses: the base category does not need fibre products and the Beck-Chevalley condition, in the form of a natural transformation, can be weakened by only requiring the latter to be epi.
Final version, to appear in Cahiers de topologie et géométrie différentielle catégoriques