= Relative homotopy of a Serre fibration
{title2=$\pi_n(E,F)\cong\pi_n(B)$}
For a based <Serre fibration> with fibre $F$ over the basepoint, lift a based cube in $B$ from its constant bottom face, keeping the side faces fixed. Its final face lies in $F$, giving surjectivity of the relative map. <Homotopies> in $B$ lift; two lifts of the same cube are relatively homotopic by lifting with both side liftings prescribed. This gives injectivity. For $n\ge2$ this is a <group> <isomorphism>; at $n=1$ it is initially a bijection of <pointed sets>, unless the relative set is endowed with the <group> law transported through the fibration.
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