caa a22 4500 44537893X CHVBK 20180317143011.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10485-009-9217-0 doi (NATIONALLICENCE)springer-10.1007/s10485-009-9217-0 The Eilenberg-Moore Category and a Beck-type Theorem for a Morita Context [Elektronische Daten] [Tomasz Brzeziński, Adrian Vazquez Marquez, Joost Vercruysse] 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. Springer Science+Business Media B.V., 2009 Monad nationallicence Adjoint functor nationallicence Morita context nationallicence Eilenberg-Moore category nationallicence Brzeziński Tomasz Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK aut Vazquez Marquez Adrian Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK aut Vercruysse Joost Faculty of Engineering, Vrije Universiteit Brussel (VUB), 1050, Brussels, Belgium aut Applied Categorical Structures Springer Netherlands 19/5(2011-10-01), 821-858 0927-2852 19:5<821 2011 19 10485 https://doi.org/10.1007/s10485-009-9217-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-009-9217-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brzeziński Tomasz Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK aut NATIONALLICENCE 700 1- Vazquez Marquez Adrian Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK aut NATIONALLICENCE 700 1- Vercruysse Joost Faculty of Engineering, Vrije Universiteit Brussel (VUB), 1050, Brussels, Belgium aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/5(2011-10-01), 821-858 0927-2852 19:5<821 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer