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HomoMorphism

A homomorphism, from one mathematical object to another of the same kind, is a function that preserves all relevant structure.  For instance, if we are concerned about some operation *, homomorphisms must satisfy f(x*y)=f(x)*f(y).

A homomorphism which is also OneToOne is called an IsoMorphism; two isomorphic objects are completely indistinguishable as far as the structure in question is concerned.  A homomorphism from a set to itself is called an EndoMorphism, and if it is also an isomorphism is called an AutoMorphism.