The adaptation of artificial intelligence systems concepts to knowledge representation formalisms fundamental invariants is studied. The abstract knowledge inclusion and composition invariants of such formalisms used to be the main tools for simulating the knowledge semantic and algebraic structures. Formal analysis of these invariants provides specialists with a new application domain for developing the abstract mathematical systems general theory. This application relates to informal concept of knowledge processing operations and is based on fundamentals of linguistics, psychology, pedagogics and philosophy. Different classes of morphisms, usual for set theory, formal logic, abstract algebra, theory of algorithms and topology, are used for simulating such operations. Universal Blums classification of cognitive operations and goals used to be the completeness and independence criteria for introduced morphisms classification. Simulating of cognitive processes non-formal invariants by abstract morphisms classification for knowledge representation formalisms is realized by morphisms compositions considered as patterns of cognitive goals realizations within formalisms of abstract knowledge spaces. Such compositions define complex knowledge synthesis processes, based on subject domain elementary and simple knowledge sets, represented by knowledge area ontology. The morphisms formal classification agrees with the different types of weakly formalized cognitive goals and the thinking processes that search for such goals realizations. An application is proposed for morphisms compositions at artificial intelligent systems based on abstract morphisms transformation and realized as morphisms homomorphic extensions into professional tasks solution processes. An example of such a process is provided for creation of the products manufacturing plan. Product of every type is made by the sequence of products process­ing operations performed on machines with known properties and attributes. Morphisms composition engineering originates the plan-creating process. This process uses three general types of morphisms for complex knowledge synthesis processes represented by knowledge integration, knowledge transformation and knowledge tracing.