Sheaves on subanalytic sites (Q2389049)

Let \(k\) be a field and \(X\) be a real analytic manifold. The spaces of functions which are not defined by local properties do not define sheaves on \(X\), they define sheaves on a site associated to \(X\), the subanalytic site \(X_{sa}\). \textit{M. Kashiwara} and \textit{P. Schapira} [Ind-sheaves. Astérisque. 271. Paris: Société Mathématique de France (2001; Zbl 0993.32009)] introduced the notion of ind-sheaves and defined the so-called six Grothendieck operations in this framework. Restriction to \(\mathbb{R}\)-constructible sheaves gives an equivalence between the category of ind \(\mathbb{R}\)-constructible sheaves on \(X\) and the categroy \(\text{Mod}(k_{X_{sa}})\) of sheaves on the subanalytic site associated to \(X\). The paper gives a direct, self-contained construction of the six Grothendieck operations on \(\text{Mod}(k_{X_{sa}})\) without using the theory of ind-sheaves.