A category over is a prefibered category if for every morphism there is a weakly cartesian morphism with .
This differs from a fibered category by not requiring that a composition of weakly cartesian morphisms is weakly cartesian, or equivalently that strongly cartesian liftings exist.
Just as a fibred category corresponds to a pseudofunctor , a prefibred category corresponds to a normal lax functor . For constrast, every functor into is a normal lax functor , see at displayed category.
Prefibered (prefibred) category (Rus. предрасслоённая категория, Fr. catégorie préfibrée)
Last revised on January 19, 2023 at 17:59:30. See the history of this page for a list of all contributions to it.