NDLI: Von Neumann Categories

Content Provider	Springer Nature Link
Author	Blute, Richard Comeau, Marc
Copyright Year	2014
Abstract	We introduce the notion of a von Neumann category, as a multi-object version of von Neumann algebra. A von Neumann category is a premonoidal category with compatible ∗-structure which embeds as a double commutant into a suitable premonoidal category of Hilbert spaces. The notion was inspired by algebraic quantum field theory, and we do explain that basic idea and indicate how quantum teleportation could be encoded in this setting. But we focus here on the structure of von Neumann categories. After giving the definitions and examples, we consider constructions typically associated to von Neumann algebras, and examine their extensions to the category-theoretic setting. In particular, we present a crossed product construction for ∗-premonoidal categories.
Starting Page	725
Ending Page	740
Page Count	16
File Format	PDF
ISSN	09272852
Journal	Applied Categorical Structures
Volume Number	23
Issue Number	5
e-ISSN	15729095
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-07-10
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Logic and Foundations Theory of Computation Convex and Discrete Geometry Geometry
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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Von Neumann Categories