Noncommutativity as a colimit

Details Noncommutativity as a colimit Noncommutativity as a colimit

2010-03-18

arxiv.org/abs/1003.3618v3

Mathematics

Category Theory

22 pages; updated theorem 15, added propoisition 36

Scientific paper

10.1007/s10485-011-9246-3

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.

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