Orthomodular lattices, Foulis Semigroups and Dagger Kernel Categories

Understand

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 current categorical perspective gives a broader context and reconstructs this relationship between orthomodular lattices and Foulis semigroups as special instance.