A cobordism category $Cob$ typically is canonically a dagger-category with dagger-involution given by reversal of the orientation of cobordisms.
Given a symmetric monoidal dagger category $\mathcal{C}$ as coefficients, a 1-functorial field theory
is called “unitary” if it is a dagger functor.
(This is the “hermitian axiom” of Atiyah 1989.)
The original notion:
Michael Atiyah, p. 8 of: Topological quantum field theories, Publications Mathématiques de l’IHÉS 86 (1989) 175-186 [numdam:PMIHES_1988__68__175_0]
Vladimir Turaev, Hermitian and unitary TQFTs, §III.5 in: Quantum invariants of knots and 3-manifolds, Studies in Mathematics 18, de Gruyter (1994) [doi:10.1515/9783110435221]
Exposition and review:
Further discussion:
On generalization to extended functorial field theory via higher dagger categories:
See also:
Last revised on January 17, 2024 at 15:37:17. See the history of this page for a list of all contributions to it.