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Category theory has been recently used as a tool for constructing andmodeling an information flow framework. Here, we show that the flow ofinformation can be described using preradicals. We prove that preradicalsgeneralize the notion of persistence in spaces where the underlying structureforms a directed acyclic graph. We show that a particular $\alpha$ preradicaldescribes the persistence of a commutative $G$-module associated with adirected acyclic graph. Furthermore, given how preradicals are defined, theyare able to preserve the modeled system's underlying structure. This allows usto generalize the notions of standard persistence, zigzag persistence, andmultidirectional persistence.

A category theory approach using preradicals to model information flows in networks