Given a functor \(F \colon \mathcal C\rightarrow\mathcal D\) of \(\infty\)-categories, by [Lur17, Rmk. 5.3.1.4] the centralizer in \(\mathrm{Cat}_{\infty}\) exists and is given by the functor category \(\mathrm{Fun}(\mathcal C, \mathcal D)\) with pointing \(u \colon \{F\} \rightarrow\mathrm{Fun}(\mathcal C, \mathcal D)\) and \(\mathrm{ev}\colon \mathrm{Fun}(\mathcal C, \mathcal D) \times \mathcal C\rightarrow\mathcal D\) given by the evaluation functor.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2