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In [1], given a 2-category A satisfying suitable hypothesis, we give the semantic factorization via descent. This specializes to a new connection between monadicity and descent theory, which can be seen as a counterpart account to the celebrated Bénabou-Roubaud Theorem [2]. It also leads in particular to a (formal) monadicity theorem. The result is new even in the case of the Eilenberg-Moore factorization of a functor that has a left adjoint in Cat. In this talk, we shall give a sketch of the ideas and constructions involved in this particular case. We give focus on the monadicity theorem and, if time allows, we give an application in the context of [2,3]: namely, one of the directions of the implications of the Bénabou-Roubaud Theorem does not depend on the Beck-Chevalley condition. [1] F. Lucatelli Nunes. Semantic Factorization and Descent. (in preparation) [2] J. Bénabou and J. Roubaud, Monades et descente, C. R. Acad. Sci. Paris Sr. A-B 270 (1970) A96-A98. [3] G. Janelidze and W. Tholen. Facets of Descent I, Applied Categ. Structures 2 (1994), no.3, 245-281.
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