# A note on unitizations of generalized effect algebras

## TL;DR

This paper demonstrates that the process of unitization in generalized effect algebras forms a monadic adjunction with the forgetful functor to effect algebras, establishing a categorical foundation for the construction.

## Contribution

It proves that the unitization functor is a left adjoint to the forgetful functor and that this adjunction is monadic, clarifying the categorical relationship.

## Key findings

- The forgetful functor is a right adjoint.
- The unitization construction is the left adjoint.
- The adjunction is monadic.

## Abstract

There is a forgetful functor from the category of generalized effect algebras to the category of effect algebras. We prove that this functor is a right adjoint and that the corresponding left adjoint is the well-known unitization construction by Hedl\'ikov\'a and Pulmannov\'a. Moreover, this adjunction is monadic.