Equivariant sheaves for profinite groups

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. resolve a serious deficit in existing theory by constructing good notion of presheaves, with suitable sheafification functor. Using sheafification, we develop general modules ring, give explicit constructions infinite products and introduce an analogue skyscraper sheaves. These results underlie recent work authors which proves that there algebraic model for rational G-spectra terms spaces. That constructed Weyl-G-sheaves space closed subgroups G, term Weyl indicates stalk H H-fixed. In this paper, prove R-modules form abelian category enough injectives coreflective subcategory R-modules. end paper structural result provides another way conveniently build from simpler data. G-equivariant sheaf base X colimit finite discrete spaces Xi actions groups Gi, limit G Gi.