Smash product of CW pairs ($(X,A)\wedge (Y,B)=(X\times Y,(A\times Y)\cup (X\times B))$)

The quotient of the displayed CW pair is $(X/A)\wedge (Y/B)$. In a multiplicative generalized cohomology theory, external products of relative classes of degrees $k,m$ take values in degree $k+m$ of this pair. Pullback along a diagonal produces the relative cup product.