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This paper is a sequel to arXiv:0902.2355 and continues the study of quantumlogic via dagger kernel categories. It develops the relation between thesecategories and both orthomodular lattices and Foulis semigroups. The relationbetween the latter two notions has been uncovered in the 1960s. The currentcategorical perspective gives a broader context and reconstructs thisrelationship between orthomodular lattices and Foulis semigroups as specialinstance.

Orthomodular lattices, Foulis Semigroups and Dagger Kernel Categories