The net of map $f \colon \Delta \to \Gamma$ between abstract simplicial complexes is a list of variables in the ring of $\Gamma$. This list determines a ring map from the ring of $\Delta$ to the ring of $\Gamma$ by sending the $i$-th variable in the ring of $\Delta$ to the $i$-th monomial on the list.
The identity map $\operatorname{id} \colon \Delta \to \Delta$ corresponds to list of variables in the ring of $\Delta$.
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The next example does not come from the identity map.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/SimplicialComplexes/Documentation.m2:3866:0.