On the Mathematical Structure of Cascade Effects and Emergent Phenomena

We argue that the mathematical structure, enabling certain cascading and emergent phenomena to intuitively emerge, coincides with Galois connections. We introduce the notion of generative effects to formally capture such phenomena. We establish that these effects arise, via a notion of a veil, from either concealing mechanisms in a system or forgetting characteristics from it. The goal of the work is to initiate a mathematical base that enables us to further study such phenomena. In particular, generative effects can be further linked to a certain loss of exactness. Homological algebra, and related algebraic methods, may then be used to characterize the effects.