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

Abstract

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