General morphism for modeling relations in multimodeling

Multimodeling represents a recent remarkable progress in modeling methodology. It includes new types of relationships between models, which cannot be formulated as usual homomorphisms. First this paper identifies the three types of morphism for the modeling relations involved in multimodeling: homomorphism-type, refinement-type, and integration-type. The morphism that can deal with all the types is required to have the properties of partiality and behavior preservation as well as structure preservation. This paper develops a rigorous framework of general morphism for modeling theory so as to provide a formal device that fulfills such requirements and represents all the types of relationships between models including the relationships among experimental frame, real system, base model, lumped model in modeling theory, as well as those involved especially in multimodeling.