Generative Category Theory

This paper proposes a research framework for generative category theory. We define the category GenCat of stable generative objects, in which a morphism carries a parameter of admissible structural tension. On this basis we formulate generative functors, natural transformations, limits, adjunctions, and a category of scales. The central aim is to describe the coordination of generative structures through explicit invariant-preservation conditions, rather than through abstract arrows lacking an operational interpretation. Definitions and their classical consequences are kept separate from programmatic principles and hypotheses; the sections on sheaves, topoi, adjunctions, and higher categories have the status of directions for further development.