A functor is of descent type if it satisfies “half” of the condition to be monadic.
A functor is of descent type if
The second condition is equivalent to asking that the comparison functor from to the Eilenberg-Moore category of the monad is fully faithful.
By monadic descent, a morphism in the base of a fibration is a descent morphism if and only if is of descent type. This is presumably the origin of the terminology; is an effective descent morphism when is monadic.
Last revised on June 26, 2017 at 12:43:17. See the history of this page for a list of all contributions to it.