= Category of rings
{title2=$\mathbf{Rng}$}
The category of unital <rings> has identity-preserving <ring homomorphisms> as morphisms. The zero ring, allowing $0=1$, is terminal, and $\mathbb Z$ is initial. Nonzero rings admit no maps from the zero ring. Monomorphisms are injective: maps from $\mathbb Z[x]$ probe individual elements. It is a <regular category>, with surjective homomorphisms as <regular epimorphisms>; these are distinct from arbitrary categorical <epimorphisms>.
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