Monoidal categories and beyond: new contexts and new applications

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The project aims to develop a theory of generalised monoidal structures with applications to fields as diverse as combinatorics, representation theory, algebraic geometry, topology, theoretical physics and computer science. Monoidal categories are a mathematical formalism for systems with operations of parallel and serial composition, such as the Hilbert space model of quantum mechanics. Recent developments in topology and quantum algebra have led to more general notions of monoidal category, and further progress requires a comprehensive theory of such structures.