We define Frobenius-Eilenberg-Moore objects for a dagger Frobenius monad in an arbitrary dagger 2-category, and extend to the dagger context a well-known universal property of the formal theory of monads. We show that the free completion of a 2-category under Eilenberg-Moore objects extends to the dagger context, provided one is willing to work with those dagger Frobenius monads for which the endofunctor suitably commutes with the unit. Finally, we define dagger lax functors and dagger lax-limits of such functors, and show that Frobenius-Eilenberg-Moore objects are examples of such limits.
Keywords: Dagger category, Frobenius monad, Lax functor, Kleisli category, Eilenberg-Moore category
2020 MSC: 18A35, 18A40, 18C15, 18C20, 18D70, 18N10, 18N15
Theory and Applications of Categories, Vol. 37, 2021, No. 31, pp 996-1016.