Functor Models: A Structural Generalization of Function Models

This note introduces Functor Models as a structural generalization of Function Models. A Function Model is typically expressed as a morphism . A Functor Model is a functor, where the source and target categories are designed to represent canonical specifications, transformations, executable artifacts, and validated runtime changes. The functorial laws encode compositional correctness and allow results proved at the functor level to specialize automatically to the function level. Stochastic and hybrid regimes are accommodated via distribution-valued lifts, yielding a principled boundary between deterministic function models and inherently stochastic kernels.