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  "body": "\n## Summary\n\nA generalized (or extraordinary) cohomology theory is a contravariant functor from pairs of spaces to graded abelian groups.\nIt satisfies all the [[Eilenberg–Steenrod axioms|YHK51GHK2T]] except the dimension axiom.\nSo the cohomology of a point may be nonzero in many degrees.\nTopological K-theory, complex cobordism and stable cohomotopy are the main examples, and each such theory is represented by a spectrum.\n\n## Explanations\n\n### L1 human\n\nOrdinary cohomology gives a point only one nonzero group, in degree $0$.\nSome useful invariants of spaces behave exactly like cohomology in every other way, but give a point a whole sequence of nonzero groups.\nThese are the generalized cohomology theories.\nFor example, complex K-theory, built from vector bundles, assigns to a point the integers in every even degree and zero in every odd degree.\n",
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