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Bases as Coalgebras

Bart Jacobs.

The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier work). It is illustrated how such coalgebras-on-algebras can be&nbsp;[&hellip;]

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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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Relating Apartness and Bisimulation

Herman Geuvers ; Bart Jacobs.

A bisimulation for a coalgebra of a functor on the category of sets can be described via a coalgebra in the category of relations, of a lifted functor. A final coalgebra then gives rise to the coinduction principle, which states that two bisimilar elements are equal. For polynomial functors, this&nbsp;[&hellip;]

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