Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Lucatelli Nunes, Fernando2024-10-172024-10-172023https://oa.tib.eu/renate/handle/123456789/16990https://doi.org/10.34657/16012Let A be a 2-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism p exists and is preserved by a suitable morphism, the factorization given by the lax descent object of the higher cokernel of p is up to isomorphism the same as the semantic factorization of p, either one existing if the other does. The result can be seen as a counterpart account to the celebrated Bénabou-Roubaud theorem. This leads in particular to a monadicity theorem, since it characterizes monadicity via descent. It should be noted that all the conditions on the codensity monad of p trivially hold whenever p has a left adjoint and, hence, in this case, we find monadicity to be a 2-dimensional exact condition on p, namely, to be an effective faithful morphism of the 2-category A.engformal monadicity theoremformal theory of monadscodensity monadssemantic lax descent factorizationdescent datatwo-dimensional cokernel diagramopcomma objecteffective faithful morphismBénabou-Roubaud theoremlax descent categorytwo-dimensional limits510Report