@UNPUBLISHED{publication1, title = "Semantic factorization and descent", author = "{LUCATELLI NUNES, Fernando}", year = "2019-02-01", abstract = " Let A be a 2-category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 B\énabou-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 a 2-effective monomorphism of the 2-category A. ", url = "http://www.mat.uc.pt/preprints/eng\_2019.html", note = "" }