The Eilenberg-Moore category and a Beck-type theorem for a Morita context

Details The Eilenberg-Moore category and a Beck-type theorem for a Morita context The Eilenberg-Moore category and a Beck-type theorem for a Morita context

2008-11-26

arxiv.org/abs/0811.4304v2

Mathematics

Category Theory

33 pages, some corrections, new section 5.3

Scientific paper

The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a {\em 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 {\em 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 {\em moritability} of a pair of functors with a common domain) are derived.

Affiliated with

Also associated with

No associations

Rating

The Eilenberg-Moore category and a Beck-type theorem for a Morita context does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Eilenberg-Moore category and a Beck-type theorem for a Morita context, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Eilenberg-Moore category and a Beck-type theorem for a Morita context will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274537