Abstract
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.
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Communicated by Y. Kawahigashi
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Heunen, C. Characterizations of Categories of Commutative C*-Subalgebras. Commun. Math. Phys. 331, 215–238 (2014). https://doi.org/10.1007/s00220-014-2088-8
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DOI: https://doi.org/10.1007/s00220-014-2088-8