Definition 19.6.1 ([Lurie (2017), Definition 4.7.0.1]). A monad on an \(\infty \)-category \(C\) is an associative algebra object \[ T \in \Alg (\Fun (C,C)) \] for the composition monoidal structure. Its Eilenberg–Moore category is the \(\infty \)-category \[ \LMod _T(C) \] of left \(T\)-module objects in \(C\), formed using the evaluation left tensoring constructed above. It comes with a forgetful functor \(U_T\colon \LMod _T(C) \to C\).
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