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 $Y = Y_1 \cap \cdots \cap Y_k$
