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Mar 13, 2012 at 21:25 comment added Jan Weidner While constructible sheaves are combinatorial as you say, the constructible derived category, which is the interesting object from viewpoint of sheaf cohomology is not! It is not the derived category of constructible sheaves, but the full subcategory of the derived category of all sheaves consisting of objects with constructible cohomology. Therefore complicated sheaves are always present in the backstage.
Jul 20, 2010 at 22:20 history answered algori CC BY-SA 2.5