Applied Categorical Structures

, Volume 20, Issue 4, pp 393–414 | Cite as

Noncommutativity as a Colimit

Open Access
Article

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.

Keywords

Partial Boolean algebra Partial C*-algebra Colimit 

Mathematics Subject Classifications (2010)

16B50 18A30 46L05 46L85 06E15 81P16 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Oxford University Computing LaboratoryOxfordUK

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