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 .
Prefibered (prefibred) category (Rus. предрасслоённая категория, Fr. catégorie préfibrée)
See also foliated category, fibered category
Last revised on May 12, 2017 at 03:38:34. See the history of this page for a list of all contributions to it.