"Polynomial Functors over Groupoids: from Program Semantics to Quantum Field Theory"
Polynomial functors are essentially functors defined in terms of
sums, products, and exponentiation, and can be seen as a
categorification of elementary arithmetic. I will explain their
role in program semantics to express generic data type
constructors, and in particular inductive types, and how groupoid
coefficients allow for a type interpretation of Feynman graphs
as wellfounded trees. Inductive types are solutions to fixpoint
equations. From the viewpoint of Quantum Field Theory, these
are the combinatorial Dyson-Schwinger equations.