Abstract
We give substance to the motto “every partial algebra is the colimit of its total subalgebras” by proving it for partial Boolean algebras (including orthomodular lattices), the new notion of partial C*-algebras (including noncommutative C*-algebras), and variations such as partial complete Boolean algebras and partial AW*-algebras. Both pairs of 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 (Heunen et al. 2010), that works on partial C*-algebras, is functorial.
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C. Heunen was supported by the Netherlands Organisation for Scientific Research (NWO). Part of this work was performed while the author visited the IQI at Caltech.
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van den Berg, B., Heunen, C. Noncommutativity as a Colimit. Appl Categor Struct 20, 393–414 (2012). https://doi.org/10.1007/s10485-011-9246-3
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DOI: https://doi.org/10.1007/s10485-011-9246-3