id_Delta
The identity map on the underlying vertex set of an abstract simplicial complex induces the identity map on the entire complex.
The first example is the identity map on a $4$-simplex.
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The second example is the identity map on the octahedron.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/SimplicialComplexes/Documentation.m2:3965:0.