The categories of operator spaces, operator systems, Archimedean order unit spaces, and unital operator algebras are locally countably presentable, and unital operator algebras form the Eilenberg-Moore category of the Haagerup tensor monad.
Springer- Verlag, New York, 1985
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Local presentability and monadicity of forgetful functors for operator algebraic categories
The categories of operator spaces, operator systems, Archimedean order unit spaces, and unital operator algebras are locally countably presentable, and unital operator algebras form the Eilenberg-Moore category of the Haagerup tensor monad.