Noncommutativity as a colimit

DOI10.1007/S10485-011-9246-3zbMath1261.46051arXiv1003.3618OpenAlexW1988737084MaRDI QIDQ695318

Benno van den Berg, Chris Heunen

Publication date: 21 December 2012

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.3618

zbMATH Keywords

von Neumann algebraStone dualityprojectionlocalequantum mechanicsframetopostensor productGelfand dualitycolimitgeometric morphism(co)complete category(partial) Boolean algebracategorical reflectioncommeasurability relationpartial \(C^*\)-algebrapartial AW*-algebrapartial Rickart \(C^{\ast}\)-algebras

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Stone spaces (Boolean spaces) and related structures (06E15) Tensor products of (C^*)-algebras (46L06) Categories, functors in functional analysis (46M15) Special categories (18B99) Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) (18A30)

Related Items (11)

A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors ⋮ A categorial semantic representation of quantum event structures ⋮ The space of measurement outcomes as a spectral invariant for non-commutative algebras ⋮ Complementarity in categorical quantum mechanics ⋮ Characterizations of categories of commutative \(C^*\)-subalgebras ⋮ Active lattices determine \(\mathrm{AW}^\ast\)-algebras ⋮ The paraunitary group of a von Neumann algebra ⋮ Classifying finite-dimensional \(C^*\)-algebras by posets of their commutative \(C^*\)-subalgebras ⋮ Maps preserving products of commuting elements in von Neumann algebras ⋮ Contextual semantics in quantum mechanics from a categorical point of view ⋮ From Quantum-Mechanical Lattice of Projections to Smooth Structure of $$\mathbb {R}^4$$R4

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A factor not anti-isomorphic to itself
• Quantum logic in algebraic approach
• Kochen-Specker theorem for von Neumann algebras
• “What is a Thing?”: Topos Theory in the Foundations of Physics
• Completely positive maps into corona algebras
• On the Lattice of Subalgebras of a Boolean Algebra

This page was built for publication: Noncommutativity as a colimit