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Definition

A dagger category is a dagger precategory such that for all $a,b:A$, the function $idtouiso_{a,b}$, as defined in the dagger precategory article, is an equivalence.

The inverse of $idtouiso$ is denoted $uisotoid$.

Examples

• Every groupoid is a dagger category with $f^\dagger = f^{-1}$.

• The dagger category $Rel$ of sets and relations is a dagger category with $f^\dagger$ representing the opposite relation of a relation $f$.

• The dagger category $Hilb$HilbR of Hilbert spaces over the real numbers and linear functions maps is a dagger category with$f^\dagger$ representing the adjoint linear function map of$f$.

See also

• Category theory

References

• HoTT book