Deformation Theory for $(\mathrm{\infty },n)$-categories

For an $(\mathrm{\infty },n)$-category $\mathcal{E}$ we define an $(\mathrm{\infty },1)$ category $\mathrm{T}\mathrm{w}\mathrm{A}\mathrm{r}(\mathcal{E})$ and provide an isomorphism between the stabilization of the overcategory of $\mathcal{E}$ in ${\mathrm{C}\mathrm{a}\mathrm{t}}_{(\mathrm{\infty },n)}$ and the $\mathrm{\infty }$-category of spectrum-valued functors on $\mathrm{T}\mathrm{w}\mathrm{A}\mathrm{r}(\mathcal{E})$. We use this to develop the deformation theory of $(\mathrm{\infty },n)$-categories and apply it to given an $\mathrm{\infty }$-categorical characterization of lax-idempotent monads.