Noncommutativity as a colimit
Category Theory
2012-12-05 v3 Operator Algebras
Quantum Physics
Abstract
Every partial algebra is the colimit of its total subalgebras. We prove this result for partial Boolean algebras (including orthomodular lattices) and the new notion of partial C*-algebras (including noncommutative C*-algebras), and variations such as partial complete Boolean algebras and partial AW*-algebras. The first two results are related by taking projections. As corollaries we find extensions of Stone duality and Gelfand duality. Finally, we investigate the extent to which the Bohrification construction, that works on partial C*-algebras, is functorial.
Cite
@article{arxiv.1003.3618,
title = {Noncommutativity as a colimit},
author = {Benno van den Berg and Chris Heunen},
journal= {arXiv preprint arXiv:1003.3618},
year = {2012}
}
Comments
22 pages; updated theorem 15, added propoisition 36