nLab symmetric monoidal dagger category

Definition

A symmetric monoidal dagger category is a braided monoidal dagger category $C$ which is also a symmetric monoidal category, i.e. such that for all objects $A \in Ob(C)$ and $B \in Ob(C)$, $\beta_{A,B} \circ \beta_{B, A} = \Iota_{A,B}$.

Examples

• compact closed dagger category

• symmetric monoidal groupoid, 2-group

See also

• dagger category

• monoidal dagger category

• braided monoidal dagger category

• symmetric monoidal category