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Relative subanalytic sheaves

Teresa Monteiro Fernandes, Luca Prelli (2014)

Fundamenta Mathematicae

Given a real analytic manifold Y, denote by Y s a the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor S on the category of sheaves on Y s a and study its properties. Roughly speaking, S is a sheaf on X s a × S . As an application, one can now define sheaves of functions on Y which are tempered or Whitney in the relative sense, that is, only with respect to X.

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