Triangulated categories for the analysts

This paper aims at showing how the tools of Algebraic Geome-try apply to Analysis. We will review various classical constructions, including Sato’s hyperfunctions, Fourier-Sato transform and microlo-calization, the microlocal theory of sheaves (with some applications to PDE) and explain the necessity of Grothendieck topologies to treat algebraically generalized functions with growth conditions. Mathematics Subject Classification: 58G07, 32A45, 32C38, 35A2