The ring homomorphism "η" appearing in the above is often called a structure map. In the commutative case, one can consider the category whose objects are ring homomorphisms "R" → "A"; i.e., commutative "R"-algebras and whose morphisms are ring homomorphisms "A" → "A" that are under "R"; i.e., "R" → "A" → "A" is "R" → "A" (i.e., the coslice category of the category of commutative rings under "R".) The prime spectrum functor Spec then determines an anti-equivalence of this category to the category of affine schemes over Spec "R".