Given a variety $X$ and a complete-intersection morphism
$$
Y \to X
$$
is there an analogue of the Koszul complex for $\mathcal{O}_Y \in \textbf{Coh}(X)$ in the setting of constructible sheaves? Meaning, if I consider the constant constructible sheaf
$$
\underline{\mathbb{Q}}_{Y}
$$
does there exist a complex of constructible sheaves analogous to the koszul complex?

---
I thought about this more and realized there is a complex of constructible sheaves
$$
0 \to \underline{\mathbb{Q}}_{X-Y} \to \underline{\mathbb{Q}}_X \to \underline{\mathbb{Q}}_Y \to 0
$$
I expect the first two terms to be flat since their stalks are one-dimensional and they have trivial monodromy. But this makes me a little uncomfortable because I was expecting to take a repeated derived intersection
$$
\underline{\mathbb{Q}}_{Y_1}\otimes^\mathbf{L} \cdots \otimes^{\mathbf{L}}\underline{\mathbb{Q}}_{Y_k}
$$
where $Y = Y_1 \cap \cdots \cap Y_k$