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Restricting our attention to the 2-category of categories, the main result of [1] gives in particular a natural factorization of functors via descent. Moreover, under suitable hypothesis, this factorization is shown to coincide with the semantic factorization of the functor. This gives as a consequence a connection between (co)monadicity and descent that can be seen as a counterpart account to the celebrated Bénabou-Roubaud Theorem [2]. Despite the title, I shall not assume any knowledge from my previous talk. Instead, I shall talk about the main result of [1] in the particular case of right/left adjoint functors, under a different perspective - a direct approach/analogy with the 1-dimensional case.
[1] F. Lucatelli Nunes. Semantic Factorization and Descent. arXiv:1902.01225 (2019).
[2] J. Bénabou and J. Roubaud, Monades et descente, C. R. Acad. Sci. Paris Sr. A-B 270 (1970) A96-A98.
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