  Given a ring $R$, we have a classical result stating that the ordinary
category of modules is the abelianization of the category of augmented
$R$-algebras. Analogously, using the framework of infinity categories and
higher algebra, Francis showed that the infinity category of $R$-modules is the
stabilization of the infinity category of augmented $R$-algebras. In this work
we show a dual result for coalgebras over a cooperad $Q$: namely that given a
coalgebra $C$, comodules over $C$ are the costabilization of coalgebras over
$C$, which is the universal stable category with a finite colimit preserving
functor to coalgebras over $C$.
