A many-to-one mapping of some characteristics of a concrete system onto a model of the same.
An homomorphism is an imperfect, partial or limited isomorphism. K. KRIPPENDORFF writes: "Homomorphisms are important in establishing whether one system is a model of another and which properties of the original of the system the model retains. For each system one can construct a lattice of homomorphic simplifications" (1986, p.36).
G. KLIR explains: "An homomorphic relation between two systems is contingent upon a function from relevant entities of one system (the original) onto the corresponding entities of the other system (the modelling system) under which the relation among entities is preserved. If the function, which is called a homomorphic function, is bijective, the relation is preserved completely (we say that the two systems are isomorphic); otherwise it is preserved only in a simplified form" (1993, p.30).
The last case is by far the most common.
R. VALLÉE, refering himself to the example of "the map, which is not the territory" (KORZYBSKI) states: "The map is not supposed to provide useless details. Homomorphism is enough, and the degree of accuracy of a representation ought to be adapted to the purpose for which it has been chosen: cognition, action or any other end" (1991, p.4).
V. TURCHIN makes the suggestive comment – helpful in placing models in proper perspective – that: "A model is a family of homomorphisms" (1993, p.7).
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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