Harmony and Precision of the Research Method by Fundaments: More Commutative Algebra and Consistence Theorems

As has been mentioned in many expositions and international publications, the research method by fundaments is determined and established as a derived categories scheme on a commutative ring, whose morphisms between categories have inverses, conforming quasi-isomorphisms among the categories of the research method such as are the theory ThΣ, a true propositions set Φα , the sub-theory subThΣ, prototypes {πj }, etcetera, which are nodes of the flow diagram of the research method by fundaments. The direct morphisms, as well as the inverses demonstrate isomorphisms in commutative diagrams to consistence theorems which define the harmoniousness and precision in the functioning of the research method by foundations, even in the order of the experimentation and design of applied theories in scientific research.