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Orthomodular lattices, Foulis Semigroups and Dagger Kernel Categories

Bart Jacobs.

This paper is a sequel to arXiv:0902.2355 and continues the study of quantum logic via dagger kernel categories. It develops the relation between these categories and both orthomodular lattices and Foulis semigroups. The relation between the latter two notions has been uncovered in the 1960s. The&nbsp;[&hellip;]

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A Recipe for State-and-Effect Triangles

Bart Jacobs.

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an adjunction between state- and predicate-transformers. The&nbsp;[&hellip;]

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Hyper Normalisation and Conditioning for Discrete Probability Distributions

Bart Jacobs.

Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description of normalisation is given as a&nbsp;[&hellip;]

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