Reduced cohomology
= Reduced cohomology
{title2=$\widetilde H^*(X;R)$}
For a based space, reduced cohomology removes the coefficient-ring summand coming from the basepoint. In nonnegative degrees it is the kernel of restriction $H^*(X;R)\to H^*(\{x_0\};R)$. It agrees with ordinary <cohomology> in positive degrees and admits the <suspension isomorphism> and exact sequences for based cofibrations.