Monadic descent

In mathematics, especially category theory, a monadic descent is roughly an idea to encode descent data using a monad.

Bénabou-Roubaud theorem

The Bénabou-Roubaud theorem says that (roughly) given a bifibration satisfying the Beck–Chevalley condition for p, the category of descent data is canonically equivalent to the category of algebras of the monad induced by $p_{!},p^{*}$.

See also

• Beck's monadicity theorem

Further reading

• -English translation of Bénabou&Roubaud(1970).