phi = map f
Every simplicial map sends the vertices of the source of $f$ to the vertices of the target of $f$. Consequently, this determines a ring map between the ring of the source of $f$ and the ring of the target of $f$.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/SimplicialComplexes/Documentation.m2:3764:0.