  We show Goodwillie's calculus of functors and $n$-geometric $D^{-}$-stacks
share similar features by starting to focus on the convergence of Taylor towers
for homotopy functors and the fact that $\mathbb{R} F(A) \cong \text{holim}
\mathbb{R} F(A_{\leq n})$ for geometric stacks, where $\{ A_{\leq n} \}$
provides a Postnikov tower of some given $A \in s \text{k-Alg}$. From there we
show parallel results, such as similar homotopy fibers of connecting maps in
towers, as well as polynomial approximations, pointwise approximations and
reconstruction theorems for towers.
