It is straight-forward to verify that for a monoidal functor \(F \colon \mathcal C\rightarrow\mathcal D\) between ordinary monoidal \(1\)-categories, the centralizer \(Z_1(F) \in \mathrm{Alg}_{\mathbb E_1}(\mathrm{Cat}_1)\) in the \((2,1)\)-category \(\mathrm{Alg}_{\mathbb E_1}(\mathrm{Cat}_1)\) of monoidal \(1\)-categories is given by the category from definition 2.6.1 with unit \(1_{Z(f)}\colon {\sf pt}\rightarrow Z_1(F)\) and \(\mathrm{ev}\colon Z_1(F) \times \mathcal C\rightarrow\mathcal D\) described in definition 2.6.1 and definition 2.6.3.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2