4 problems

Fix a Lie algebra $\mathfrak{g}$ whose underlying $\Bbbk$-module is perfect. Let $\operatorname{LMod}_{\operatorname{U}(\mathfrak{g})}$ be the $\infty$-category of left modules ove…

Let $\operatorname{Grp}(\operatorname{Lie}_{\Bbbk})$ be the $\infty$-category of group objects in Lie algebras, and let … be the Tate-realization functor, denoted in the source by…

Let $\operatorname{Lie}^{\operatorname{perf}}_{\Bbbk}\coloneqq\operatorname{Alg}_{\operatorname{Lie}}(\operatorname{Perf}_{\Bbbk})$ be the $\infty$-category of Lie algebras whose u…

Let $\Bbbk$ be the base ring. Write $\operatorname{Lie}_{\Bbbk}$ for the $\infty$-category of Lie algebras, and let…