Morphisms general properties of geometrical models

Abstract The notion “modeling” is one of the most significant in modern science. At present the approach is dominating, under which the model is understood as a set of given collection of relations in it. It is supposed that some abstraction of identification exists allowing to identify a real object with artificially created model; for all that it is more often used isomorphism and homomorphism for the relation identification. With the notion ‘modeling’ a principally new method of scientific knowledge is used that is the ‘mathematical experiment’, taking an intermediate place between ‘classical deductive and classical experimental research methods’. Under mathematical model of a concrete object it is understood combination of equations, inequalities and other limitations and conditions for their solving, that allow in created system of co-ordinates to identify the object with the only method. Any object, except mathematical one, can have other models: geometrical, graphical, digital, linguistic and so on. Sequence of transformation of geometrical model into mathematical one and then into digital one is the sequence of homomorphism. While modeling we compare it not only with mathematical similar object i.e. the model, but with theoretical conception as well as with other suitable objects for this conception. It is shown in this article the primary geometrical model in relation to mathematical one. and the definition of geometrical modeling is given . The necessary definitions of isomorphism and homomorphism models are represented as well as examples of relations between concrete objects and their models. Definitions of full geometrical model, its complexity degrees and conditions of two models equivalence are also given.

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