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A metabolism–repair theory of by-products and side-effects

The plurality of process outputs is a genericity of Nature. In this paper, Natural Law receives a new mathematical formulation founded on two axioms: ‘Everything is a set.’ and ‘Every process is a set-valued mapping.’ I present a brief introduction to the algebraic theory of set-valued mappings, which culminates in two particular morphisms: the metabolism bundle and the imminence mapping. These are relations defined on the collection of processes of a natural system, and serve to characterize material entailment and functional entailment. Generalized metabolism is material entailment of (by-)products, and generalized repair is functional entailment of (side-)effects. Metabolism–Repair networks, hence equipped with set-valued processors, expand their role from models of biological entities to generic models of all natural systems.