Review and Constructive Definitions for Mathematically Engineered Systems as Categorical Interpretation

Abstract

An analysis was performed to compare the expressibility under category theory for algebraic aspects to systems engineering. The purpose is to replicate the developed aspects under �model-based� specification theorems. A categorical definition for �system� is constructed in the category of categories centrally defined by epimorphism & functor. Then the major theorems developed for model-based are reconstructed and whose proofs chain are presented through respective deductions from Wymore[1] and Awoday[2]. The resultant is two-fold: showing �parallel� deductive abstractions and interpreted �categorical� primitives as deductive results. Algebraic differences exist in universality, indexing, and adjoint for engineering specification, yet �system of system� construction has express under functors via graphical �diagrams�. Finally type differences both intension & extension are explored throughout, and supplementary representations are discussed in incorporating �set� and �structural� formalizations to system (engineering) aspects.