nLab unitary functorial field theory




A cobordism category CobCob typically is canonically a dagger-category with dagger-involution given by reversal of the orientation of cobordisms.

Given a symmetric monoidal dagger category 𝒞\mathcal{C} as coefficients, a 1-functorial field theory

Cob𝒞 Cob \longrightarrow \mathcal{C}

is called “unitary” if it is a dagger functor.

(This is the “hermitian axiom” of Atiyah 1989.)


The original notion:

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.