Let \(\mathcal C\) be a presentably symmetric monoidal \(\infty\)-category. For every \(A\in \mathrm{Alg}_{\mathbb E_k}(\mathcal C)\), the center in \(\mathrm{Alg}_{\mathbb E_k}(\mathcal C)\) exists [Lur17, Cor. 5.3.1.15] and will henceforth be denoted by \[Z_k(A)\in\mathrm{Alg}_{\mathbb E_1}(\mathrm{Alg}_{\mathbb E_k}(\mathcal C)) = \mathrm{Alg}_{\mathbb E_{k+1}}(\mathcal C).\] By proposition 7.4.6, the underlying \(\mathbb E_k\)-algebra of \(Z_k(A)\) agrees with the centralizer \(Z_k(\mathrm{id}_A)\) from notation 7.4.3.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2