The Eilenberg-Moore Category and a Beck-type Theorem for a Morita Context |
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Authors: | Tomasz Brzeziński Adrian Vazquez Marquez Joost Vercruysse |
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Institution: | 1.Department of Mathematics,Swansea University,Swansea,UK;2.Faculty of Engineering,Vrije Universiteit Brussel (VUB),Brussels,Belgium |
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Abstract: | The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of
a Morita context comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is shown that in many cases equivalences
between categories of algebras are induced by such Morita contexts. The Eilenberg-Moore category of representations of a Morita
context is constructed. This construction allows one to associate two pairs of adjoint functors with right adjoint functors
having a common domain or a double adjunction to a Morita context. It is shown that, conversely, every Morita context arises from a double adjunction. The comparison functor
between the domain of right adjoint functors in a double adjunction and the Eilenberg-Moore category of the associated Morita
context is defined. The sufficient and necessary conditions for this comparison functor to be an equivalence (or for the moritability of a pair of functors with a common domain) are derived. |
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