# Descent Data and Absolute Kan Extensions

@article{Nunes2019DescentDA, title={Descent Data and Absolute Kan Extensions}, author={Fernando Lucatelli Nunes}, journal={arXiv: Category Theory}, year={2019} }

The fundamental construction underlying descent theory, the lax descent category, comes with a functor that forgets the \textit{descent data}. We prove that, in any $2$-category with lax descent objects, the forgetful morphisms create all absolute Kan extensions. As a consequence, we get a monadicity theorem which says that a right adjoint functor is monadic if and only if it is, up to the composition with an equivalence, a functor that forgets descent data. In particular, within the classical…

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