Effect algebras are the Eilenberg-Moore category for the Kalmbach monad

Abstract

The Kalmbach monad is the monad that arises from the free-forgetful adjunction between bounded posets and orthomodular posets. We prove that the category of effect algebras is isomorphic to the Eilenberg-Moore category for the Kalmbach monad.

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• Dichotomy between Deterministic and Probabilistic Models in Countably Additive Effectus Theory
• Effect algebras as presheaves on finite Boolean algebras
• Orthomodular posets are algebras over bounded posets with involution