Left modules

Definition 19.1.1. Let \(C\) be a monoidal \(\infty \)-category, regarded as \(\oLMod \)-monoidal by pullback along the collapse map \(\oLMod \to \Assoc \). We denote by \[ \LMod (C) := \Alg _{\oLMod }(C) \] the \(\infty \)-category of \(\oLMod \)-algebras in \(C\). Restriction along \(\fa \) defines a functor \(\fa ^*\colon \LMod (C) \to \Alg (C) := \Alg _{\Assoc }(C)\). For an associative algebra \(A \in \Alg (C)\) we define the \(\infty \)-category \(\LMod _A(C)\) of left modules over \(A\) as the fiber