Costability of Comodules

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.