Definition 7.4.5. ([Lur17, Def. 5.3.1.6]).
Let \(\mathcal C\) be a monoidal \(\infty\)-category and \(M\) an object of \(\mathcal C\). A center \(\mathfrak{Z}(M)\) of \(M\) is a final object of the \(\infty\)-category \(\mathrm{LMod}(\mathcal C) \times_{\mathcal C} \{M\}\).