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