In mathematics, especially in homotopy theory,[1] a left fibration of simplicial sets is a map that has the right lifting property with respect to the horn inclusions
[2] A right fibration is one with the right lifting property with respect to the horn inclusions
[2] A Kan fibration is one with the right lifting property with respect to every horn inclusion; hence, a Kan fibration is both a left and right fibration.
In particular, category fibered in groupoids over another category is a special case of a right fibration of simplicial sets in the ∞-category setup.
This topology-related article is a stub.