The Born rule as structure of spectral bundles (extended abstract)
  Topos approaches to quantum foundations are described in a unified way by means of spectral bundles, where the base space is a space of contexts and each fibre is its spectrum. Differences in variance are due to the bundle being a fibration or opfibration. Relative to this structure, the probabilistic predictions of the Born rule in finite dimensional settings are then described as a section of a bundle of valuations. The construction uses in an essential way the geometric nature of the valuation locale monad. 
Bertfried Fauser, Guillaume Raynaud, Steven Vickers (School of   Computer Science, University of Birmingham)
math.CT quant-ph