Homomorphism

similarity of external form, appearance or size.

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A many-to-one mapping in effect representing (see representation ) a pattern in the domain of the mapping by a simpler pattern in its range. The product of applying a homomorphism is called a homomorph. Homomorphisms are important in establishing whether one system is a model of another and which properties of the original system the model retains. For each system one can construct a lattice of homomorphic simplifications. The inverse of a homomorphism is not a mapping. (Krippendorff )