标题： 变形理论对于$(\infty,n)$-范畴 显示英文标题

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

摘要： 对于一个$(\infty,n)$-范畴$\mathscr E$，我们定义了一个$(\infty,1)$范畴$\mathrm{TwAr}(\mathscr E)$，并提供了在$\mathrm{Cat}_{(\infty,n)}$中$\mathscr E$的上范畴的稳定化与$\mathrm{TwAr}(\mathscr E)$上谱值函子的$\infty$-范畴之间的同构。 我们用它来发展$(\infty,n)$-范畴的变形理论，并将其应用于给出松弛幂等单子的$\infty$-范畴特征描述。 显示英文摘要

摘要： 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.