Associative algebras in modules not underobjects

Warning 19.2.16. There is no analogous equivalence \(\Alg (\Mod _R(C))\simeq \Alg (C)_{R/}\). Already for ordinary rings, the structure map from \(R\) to an associative algebra in \(\Mod _R(C)\) is central, whereas an arbitrary morphism from \(R\) to an associative algebra need not have central image; see also [Lurie (2017), Warning 7.1.3.9].