A Category-Theoretic Account of Phase Disjunction: Composability Conditions for Formative and Evaluative Morphisms

The original work commands the separation of formation from evaluation and forbids the circle of Structure and Necessity, yet it supplies no condition under which a recursive transition escapes that prohibition. This paper writes that condition down as three composability conditions. In a category whose objects are the formative material, the Structure and the verdict of each phase, indexed by phase, and whose morphisms are the Generative, Preservative and Evaluative Morphisms of the appendix of the original work together with the transition described in AP-X004, formation and evaluation within one phase compose in a single direction only, and a composite running from evaluation to formation is defined solely with respect to the formation of the next phase. The difference between circularity and recursion reduces to a single index on the formative morphism. Objectification is written as a forgetful functor, while no category of evaluation is set up. The formalism proves no undecidability and constructs no order of phases; it is no more than a device that performs a discrimination upon an order already given. That it constructs no order is a standing rather than a limitation, and Section 6 shows that the demand for a justification of the order does not hold, since any argument that would justify the order is already using it. This record contains both the English and the Korean edition.