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

TL;DR

This paper proves that effect algebras are categorically equivalent to the Eilenberg-Moore category of the Kalmbach monad, linking effect algebras with a specific monadic construction.

Contribution

It establishes an isomorphism between effect algebras and the Eilenberg-Moore category for the Kalmbach monad, clarifying their categorical relationship.

Findings

Effect algebras are isomorphic to the Eilenberg-Moore category for the Kalmbach monad.

The Kalmbach monad arises from the free-forgetful adjunction between bounded and orthomodular posets.

Provides a categorical characterization of effect algebras in terms of monads.

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.