Marcelo Fiore (University of Cambridge, UK), Second-Order Algebra and Generalised Polynomial Functors


  • Feb. 27, 2012, 15:00 - 16:00


The theme of this work is algebraic structure in settings richer than that of universal algebra. In this talk, I will consider an example and foundations. Starting with the example, I will introduce Second-Order Algebra: the algebra of languages with variable binding. This I will study from the viewpoints of universal algebra (equational presentations and algebraic models), equational logic (second-order deduction and rewriting), and categorical algebra (algebraic theories and functorial semantics). In this context, as well as in more general algebraic settings for languages with polymorphism and dependency, generalised polynomial functors between presheaf categories arise as foundational structures. I will present their basic theory, including differentiation.