Homologies généralisées à coefficients

If H⁎ is a generalized homology theory and A a Z-module, we can define the homology with coefficients H⁎(−,A), which is linked to the theory H⁎ by a universal coefficient exact sequence. However, this homology with coefficients is not fonctorial in A. To avoid this ambiguity, we associate with H⁎ a homology theory Hˆ⁎ that takes values in a certain Abelian category D. Hence we find a new universal coefficient exact sequence, sometimes better than the classical one.