Generalized cohomology theory
= Generalized cohomology theory
{title2=$h^n(X,A)$}
A generalized cohomology theory assigns graded groups contravariantly to suitable topological pairs, with homotopy invariance, excision and a natural long exact sequence for each pair. It omits the dimension axiom of ordinary <cohomology>, so its coefficient groups at a point can occur in degrees other than zero. A multiplicative theory also has compatible external and relative <cup products>.