= Category of commutative rings
{title2=$\mathbf{CRing}$}
The <category of commutative rings>, often written $\mathbf{CRing}$, has <commutative rings> with identity as objects and identity-preserving <ring homomorphisms> as <morphisms>. Composition and <identity morphisms> are the usual composition and identity maps. Including the <zero ring> makes it a terminal object; the <integers> form an initial object because a unique <ring homomorphism> sends $n$ to $n1_R$.
For example, a <ring homomorphism> $\mathbb Z[x]\to R$ is completely determined by the image of $x$, which can be any element of $R$. In <algebraic geometry>, applying the <spectrum of a ring> reverses arrows: a <ring homomorphism> $R\to S$ induces $\operatorname{Spec}S\to\operatorname{Spec}R$. Thus the <category of affine schemes> is equivalent to the opposite of the <category of commutative rings>.<The Stacks project>[Categories, examples of categories; Schemes, section Affine schemes]{ref}
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