Analytic non-characteristic derived Cauchy problem

Let $f:Y\to X$ be a morphism of complex manifolds, and let $Z$ be a derived $Y_{dR}$-stack that is homotopy finitely presented and non-characteristic for $f$. The natural map

$$\nu:f^{-1}\mathbb{R}\mathcal{M}ap_{Y_{dR}}(Y_{dR},Z)\longrightarrow \mathbb{R}\mathcal{M}ap_{X_{dR}}(X_{dR},f_{dR}^*Z)$$

Analytic non-characteristic derived Cauchy problem. This map is an isomorphism of sheaves of spaces over $Y$. The statement is proposed as a general nonlinear derived Cauchy-Kowalevskaya-Kashiwara problem, extending the classical analytic Cauchy-Kowalevskaya theorem; its general derived form remains open.