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We study the localization functor from the category of representation of Liesuper-algebra $\mathfrak{g} = \mathfrak{gl}(m, n)$ into monodromic D-modules onthe flag manifold $X = G/B$. We show that the right localization is monadic ina suitable sense, which identifies the coderived category of$\mathfrak{g}$-modules with the ind-completion of compactly generated$W$-modules for some algebra $W$ in monodromic $D_X$-bimodules.

Monadicity of localization for Lie super-algebras $\mathfrak{gl}(m, n)$