Sheaves on Subanalytic Sites

In Asterisque 271 the authors introduced the notion of ind-sheaf, and definedthe six Grothendieck operations in this framework. They defined subanalyticsheaves and they obtained the formalism of the six Grothendieck operations byincluding subanalytic sheaves into the category of ind-sheaves. The aim of thispaper is to give a direct construction of the six Grothendieck operations inthe framework of subanalytic sites avoiding the heavy theory of ind-sheaves. Asan application we show how to recover the subanalytic sheaves of temperate andWhitney holomorphic functions.