Definition 7.4.1. ([Lur17, Def. 5.3.1.2]).
Let \(f \colon A \rightarrow B\) be a morphism in a monoidal \(\infty\)-category \(\mathcal C\). A centralizer \(\mathfrak{Z}(f)\) of \(f\) is a final object in the \(\infty\)-category \[\mathcal C_{I/} \times_{\mathcal C_{A/}} \mathcal C_{A// B},\] where the functor \(\mathcal C_{I/} \rightarrow\mathcal C_{A/}\) sends objects \((\alpha \colon I\rightarrow X)\) of \(\mathcal C_{I/}\) to \((A \simeq I \otimes A \xrightarrow{\alpha \otimes \mathrm{id}_A} X\otimes A) \in \mathcal C_{A/}\).