Cohomology group
= Cohomology group
{title2=$H^q(C)=\ker d_q/\operatorname{im}d_{q-1}$}
A degree-$q$ cohomology group is the quotient of degree-$q$ cocycles by coboundaries in a <cochain complex>. Topological cohomology groups arise from singular or cellular cochains. Their direct sum carries the <cohomology ring> structure when equipped with the <cup product>.