1012.4526 (Chris Heunen)

On the functor l^2    [PDF]

Chris Heunen

We study the functor l^2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and both categories are enriched over algebraic domains. The functor preserves daggers, monoidal structures, enrichment, and various (co)limits, but has no adjoints. Up to unitaries, its direct image consists precisely of the partial isometries, but its essential image consists of all continuous linear maps between Hilbert spaces.

View original: http://arxiv.org/abs/1012.4526