On the Functor ℓ2

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract

We study the functor ℓ2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and in both categories homsets are 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.
Original languageEnglish
Title of host publicationComputation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky
Subtitle of host publicationEssays Dedicated to Samson Abramsky on the Occasion of His 60th Birthday
EditorsBob Coecke, Luke Ong, Prakash Panangaden
PublisherSpringer Berlin Heidelberg
Pages107-121
Number of pages15
ISBN (Electronic)978-3-642-38164-5
ISBN (Print)978-3-642-38163-8
DOIs
Publication statusPublished - 2013

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
Volume7860

Fingerprint Dive into the research topics of 'On the Functor ℓ<sup>2</sup>'. Together they form a unique fingerprint.

Cite this