Constructible is the condition that captures relationality’s core commitment: things are constituted through their relations. A configuration is constructible when every part is determined by its neighbors — no part floats free of the relational web.
Constructible arises in Movement IV: Geometric Cohesion as the test of genuine relational constitution. After stratification organizes a configuration layer by layer, constructibility asks: does each part recover from the data supplied by the parts it relates to? The forward neighborhood (what this part maps to) and the backward neighborhood (what maps to this part) together fix the part’s character. If so, the configuration contains no elements that are independent of the whole. This reflexive determination settles to a fixed point — the mutual constitution stabilizes.
Constructibility implies ambidexterity: when parts mutually determine each other, building a whole from parts (assembly from below) and constraining a whole to cohere with all parts (constraint from above) yield the same result. Neither direction has priority, because constitution is mutual.
Mathematical correspondence
Constructibility corresponds to the condition that, after Reedy fibrant replacement, every node of a diagram is reflexively determined by its matching objects in both directions. Constructibility implies the coincidence of homotopy colimits and homotopy limits.
Related
- Stratify — produces the directed structure that constructibility presupposes
- Ambidextrous — the consequence: constructibility implies ambidexterity