Abstract I argue that important generalizations in morphosyntax are currently obscured by the technical details of the syntactic apparatus. These generalizations can be brought out more clearly via a perspective that is informed by higher algebra.

I support my argument with a case study of the Person Case Constraint (PCC). I give an algebraic characterization of the attested PCCs that completely abstracts away from the details of their syntactic encoding. All PCC variants are reduced to one general prominence principle, with the cross-linguistic variation stemming from differences in how the individual person features are ranked with respect to prominence. These rankings, in turn, form a natural class in the sense that there is an algebraically natural class of functions that derives them from Zwicky’s (1977) person hierarchy. The algebraic perspective thus highlights the feature regularities that underly a specific area of morphosyntax without relying on a specific syntactic analysis.