  We establish the spin-statistics theorem for topological quantum field
theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin
structures on bordisms, and represent statistics using super vector spaces.
Unitarity is implemented using dagger categories, in a manner that is
equivalent to the approach of Freed-Hopkins, who employed
$\mathbb{Z}/2$-equivariant functors to address reflection-positivity. A key
contribution of our work is the introduction of the notion of fermionically
dagger compact categories, which extends the well-established concept of dagger
compact categories. We show that both the spin bordism category and the
category of super Hilbert spaces are examples of fermionically dagger compact
categories. The spin-statistics theorem for TQFTs emerges as a specific case of
a more general result concerning symmetric monoidal dagger functors between
fermionically dagger compact categories.
