[[!redirects symmetric monoidal dagger categories]] #Contents# * table of contents {:toc} ## Definition ## A **symmetric monoidal dagger category** is a [[braided monoidal dagger category]] $C$ with a type family $$\sigma: \beta_{(-),(-)} \circ \beta_{(-), (-)} = \Iota_{(-),(-)}$$ with dependent terms $$\sigma_{A,B}: \beta_{A,B} \circ \beta_{B, A} = \Iota_{A,B}$$ for $A:C$ and $B:C$. ## Examples ## * [[compact closed dagger category]] ## See also ## * [[Category theory]] * [[dagger category]]