Incidence-preserving map

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This term is related to: incidence geometry
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Definition

Let S and T be two incidence systems. An incidence-preserving map from S to T is a map from the set of varieties of S to the set of varieties of T that preserves the incidence relation.

In graph-theoretic terms, it corresponds to a graph homomorphism.

For the case of an incidence structure (viz an incidence system with only two types, points and blocks), if the incidence structure is connected, then every incidence-preserving map either takes points to points or blocks to blocks, or interchanges the role of points and blocks. The incidence-preserving maps that take points to ponits are termed homomorphisms and the ones that interchange the role of points and blocks are termed antihomorphisms.