n.
The ingredients of the setup are two comonads, a distributive law between them and right and left coalgebras over the distributive law.
While right coalgebras over it have an easy and known description, no similar was known for left coalgebras over it.
After recalling some background and motivation, I will explain how the latter can be obtained under some additional assumptions.
Finally, I will discuss how generalized Hopf module theorem by Mesablishvili and Wisbauer features both in theory and examples.