Fibration of simplicial sets

In mathematics, especially in homotopy theory, a left fibration of simplicial sets is a map that has the right lifting property with respect to the horn inclusions ${\displaystyle \Lambda _{i}^{n}\subset \Delta ^{n},0\leq i<n}$. A right fibration is defined similarly with the condition ${\displaystyle 0<i\leq n}$. A Kan fibration is one with the right lifting property with respect to every horn inclusion; hence, a Kan fibration is exactly a map that is both a left and right fibration.