= Brown's representability theorem
{c}
= Brown representability theorem
{c}
{synonym}
A reduced contravariant <homotopy> <functor> on based <CW complexes> satisfying the wedge-to-product axiom and the Mayer-Vietoris weak-pullback gluing axiom is represented by $[X,Y]_*$ for a <CW complex> $Y$. Half-exactness alone is not the full hypothesis. A reduced <generalized cohomology theory> supplies these axioms; suspension compatibility assembles its representing spaces into an <Omega-spectrum>.
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