Invertible weak entwining structures and weak \(C\)-cleft extensions (Q863165)

A (right) weak entwining structure is a map \(\psi:C\otimes A\to A\otimes C\) where \(A\) is an algebra and \(C\) is a coalgebra that interacts appropriately with the algebra and coalgebra structure. There is also a left version of this structure. An invertible weak entwining structure is an appropriately interacting left and right weak entwining maps with the same algebra and coalgebra. This paper studies the relationship between the left and right structures and shows that one of the conditions in the original definition of invertible weak entwining structure is redundant. It also studies \(C\)-cleft versions that utilize equilizers and coequilizers.