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## 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.

Original language | English |
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Pages (from-to) | 215-238 |

Number of pages | 24 |

Journal | Communications in Mathematical Physics |

Volume | 331 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Oct 2014 |

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## Projects

- 1 Finished