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Communications in Mathematical Physics

, Volume 357, Issue 1, pp 447–465 | Cite as

Categorial Subsystem Independence as Morphism Co-possibility

  • Zalán Gyenis
  • Miklós Rédei
Open Access
Article

Abstract

This paper formulates a notion of independence of subobjects of an object in a general (i.e., not necessarily concrete) category. Subobject independence is the categorial generalization of what is known as subsystem independence in the context of algebraic relativistic quantum field theory. The content of subobject independence formulated in this paper is morphism co-possibility: two subobjects of an object will be defined to be independent if any two morphisms on the two subobjects of an object are jointly implementable by a single morphism on the larger object. The paper investigates features of subobject independence in general, and subobject independence in the category of C*-algebras with respect to operations (completely positive unit preserving linear maps on C*-algebras) as morphisms is suggested as a natural subsystem independence axiom to express relativistic locality of the covariant functor in the categorial approach to quantum field theory.

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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of AlgebraBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of LogicEötvös Loránd UniversityBudapestHungary
  3. 3.Department of Philosophy, Logic and Scientific MethodLondon School of Economics and Political ScienceLondonUK

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