Communications in Mathematical Physics

, Volume 331, Issue 1, pp 215–238 | Cite as

Characterizations of Categories of Commutative C*-Subalgebras

  • Chris Heunen


We aim to characterize the category of injective *-homomorphisms between commutative C*-subalgebras of a given C*-algebra A. We reduce this problem to finding a weakly terminal commutative subalgebra of A, and solve the latter for various C*-algebras, including all commutative ones and all type I von Neumann algebras. This addresses a natural generalization of the Mackey–Piron programme: which lattices are those of closed subspaces of Hilbert space? We also discuss the way this categorified generalization differs from the original question.


Inverse Semigroup Closed Subspace Orthomodular Lattice Compact Hausdorff Space Commutative Subalgebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of OxfordOxfordUK

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