Divya Ahuja

We consider representations of quivers taking values in monads or comonads over a Grothendieck category $\mathcal C$. By using systems of adjoint functors between Eilenberg-Moore categories, we obtain a categorical framework of modules over monad quivers. 

We study two types of module categories over monad quiver. The first behaves like a sheaf of modules over a ringed space, and the second consists of modules that are cartesian and resemble quasi-coherent sheaves. 

Our main objective is to give conditions for these to be \textit{Grothendieck categories}. We establish similar results for comodules over a comonad quiver.