Title: Dagger Categories and Spin Statistics
Abstract: Dagger categories are categories equipped with an involution on morphisms and a notion of positivity. The most famous example is the category of Hilbert spaces, which is made out of complex vector spaces, linear maps, and the involution of taking adjoint operators. I will discuss how dagger categories let us define unitarity for functorial field theories as well as prove mathematical versions of the spin-statistics theorem in physics, which says that unitarity places constraints on the behavior of particles. This talk is inspired by joint work with Lukas Müller and Luuk Stehouwer, where we prove an extended spin statistics theorem.