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In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. This means that, given a cohomology theory
E ∗ : CW o p → Ab {\displaystyle {\mathcal {E}}^{*}:{\text{CW}}^{op}\to {\text{Ab}}} ,
there exist spaces E k {\displaystyle E^{k}} such that evaluating the cohomology theory in degree k {\displaystyle k} on a space X {\displaystyle X} is equivalent to computing the homotopy classes of maps to the space E k {\displaystyle E^{k}} , that is
E k ≅ {\displaystyle {\mathcal {E}}^{k}\cong \left}.