Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!
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.