Abelian group
Using the Eilenberg–Maclane spectrum formula_12 we can define the notion of cohomlogy of a spectrum formula_13 and the homology of a spectrum formula_13pg 42. Using the functorformula_15we can define cohomology simply asformula_16Note that for a CW complex formula_13, the cohomology of the suspension spectrum formula_18 recovers the cohomology of the original space formula_13. Note that we can define the dual notion of homology asformula_20which can be interpreted as a "dual" to the usual hom-tensor adjunction in spectra. Note that instead of formula_12, we take formula_1 for some Abelian group formula_2, we recover the usual (co)homology with coefficients in the abelian group formula_2 and denote it by formula_25.