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A dagger category is a dagger precategory such that for all , the function , as defined in the dagger precategory article, is an equivalence.
The inverse of is denoted .
Every groupoid is a dagger category with .
The dagger category of sets and relations is a dagger category with representing the opposite relation of a relation .
The dagger category of Hilbert spaces and linear functions is a dagger category with representing the adjoint linear function of .