Kerodon

Example 2.2.3.5. Let $\operatorname{\mathcal{C}}$ be a monoidal category, and let $B\operatorname{\mathcal{C}}$ be the $2$-category obtained by delooping $\operatorname{\mathcal{C}}$ (Example 2.2.2.5). Then the conjugate $2$-category $(B\operatorname{\mathcal{C}})^{\operatorname{c}}$ can be identified with $B(\operatorname{\mathcal{C}}^{\operatorname{op}})$, where we endow the opposite category $\operatorname{\mathcal{C}}^{\operatorname{op}}$ with the monoidal structure of Example 2.1.3.4.