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

Abstract

For an $(\infty ,n)$-category $\mathcal{E}$ we define an $(\infty ,1)$ category $\mathrm{TwAr}(\mathcal{E})$ and provide an isomorphism between the stabilization of the overcategory of $\mathcal{E}$ in ${\mathrm{Cat}}_{(\infty ,n)}$ and the $\infty$-category of spectrum-valued functors on $\mathrm{TwAr}(\mathcal{E})$. 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.

arXiv comment82 pages