nLab
unitary morphism

Definition

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 $f^{†}$:

$$f^{-1}=f^{†}:y\to x.$$f^{-1} = f^\dagger\colon y \to x \,.

For more details, see the entry †-category.

Examples

• The unitary morphisms in $C=$ Hilb are the ordinary unitary operators between Hilbert spaces

  In particular the unitary automorphisms of an object in $\mathrm{Hilb}$ form the unitary group.

Related concepts

• self-adjoint morphism

• unitary morphism