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Mathematics > Category Theory

arXiv:1012.4526 (math)
[Submitted on 21 Dec 2010 (v1), last revised 18 Sep 2018 (this version, v6)]

Title:On the functor l^2

Authors:Chris Heunen
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Abstract: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 its homsets are algebraic domains; the latter category has conditionally algebraic domains for homsets. 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.
Comments: 13 pages; updated Proposition 2.10
Subjects: Category Theory (math.CT); Functional Analysis (math.FA); Quantum Physics (quant-ph)
MSC classes: 46M99, 18A22, 46C07
Cite as: arXiv:1012.4526 [math.CT]
  (or arXiv:1012.4526v6 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.1012.4526
Journal reference: Computation, Logic, Games, and Quantum Foundations: 107-121, 2013
Related DOI: https://doi.org/10.1007/978-3-642-38164-5_8

Submission history

From: Chris Heunen [view email]
[v1] Tue, 21 Dec 2010 01:39:06 UTC (26 KB)
[v2] Tue, 4 Dec 2012 18:07:29 UTC (17 KB)
[v3] Thu, 21 Feb 2013 10:47:01 UTC (18 KB)
[v4] Wed, 29 Jul 2015 10:42:50 UTC (18 KB)
[v5] Tue, 22 Nov 2016 19:53:13 UTC (18 KB)
[v6] Tue, 18 Sep 2018 10:49:13 UTC (18 KB)
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