The Algebraic Structure of Morphosyntax

Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word formation, organized into a magma of morphological trees. However, unlike syntax, we do not have movement within morphology. A coproduct decomposition exists, but it requires extending the set of morphological trees beyond those which are generated solely by the magma, to a larger set of possible morphological inputs to syntactic trees. These participate in the formation of morphosyntactic trees as an algebra over an operad, and a correspondence between algebras over an operad. The process of structure formation for morphosyntactic trees can then be described in terms of this operadic correspondence that pairs syntactic and morphological data and the morphology coproduct. We reinterpret in this setting certain operations of Distributed Morphology as transformation that allow for flexibility in moving the boundary between syntax and morphology within the morphosyntactic objects.