… We define a bicategory in which the 0-cells are the entwinings over variable rings. … entwining,
is promoted here to a canonical morphism of bicategories from a bicategory of entwinings …

A weak entwining structure in a 2-category K consists of a … A weak entwining structure
can be characterized as a … -category Entw^w(K) of weak entwining structures in K. If the 2-category …

We develop a Galois (descent) theory for comonads within the framework of bicategories. We
give generalizations of Beck's theorem and the Joyal-Tierney theorem. Many examples are …

… Majid rediscovered the notion of mixed distributive laws under the name of entwining
structures ([55]). For principality, a minimal reasonable requirement is that the category of …

… We also derive the characterisation of entwining structures as liftings of Hom-functors to
module, comodule and contramodule categories; see 6.1. Finally, we study contramodules over …

… in a bicategory, we prefer to restrict to 2-categories. In the examples, instead of the bicategory
BIM… We show that also partial entwining structures in a 2-category K provide examples of a …

… Bicategory of entwinings Zoran Škoda, zskoda@irb.hr We define a bicategory in which the
0-cells are the entwinings … a given entwining, is promoted here to a canonical morphism of …

… monad and a comonad in any bicategory (the latter known as the … in is induced by a weak
entwining structure between a k-algebra … Important examples of weak entwining structures are …

… In the particular case of the monoidal bicategory of bimodules–ie … bicategory of internal
bimodules. We give a characterization of internal bialgebroids also in terms of internal entwining …

… in the mixed setup is a 2-functor from the bicategory of entwinings to a bicategory of corings.
… In the entwining case, Brzeziński and Majid combined the 4 diagrams into one picture which …