Dagger-Drazin inverses generalize Drazin inverses to arbitrary maps in dagger categories and exactly characterize Moore-Penrose invertible maps.
Azumaya (1954): Strongly π -regular rings
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Dagger-Drazin Inverses
Dagger-Drazin inverses generalize Drazin inverses to arbitrary maps in dagger categories and exactly characterize Moore-Penrose invertible maps.