In a †-category $C$, a morphism $f : x \to y$ is said to be unitary if it is invertible and its inverse $f^{-1}$ is its dagger $f^{\dagger}$:
For more details, see the entry †-category.
The unitary morphisms in $C =$ Hilb are the ordinary unitary operators between Hilbert spaces
In particular the unitary automorphisms of an object in $Hilb$ form the unitary group.
unitary morphism