Sheaves over a Diagram of S-Schemes

We say that M. (X,) is equivariant if is an isomorphism for any 4 Mor(7). Note that equivariance depends on and is not preserved by the forgetful functors in general. We denote the full subcategory of Mod(X ) consisting of equivariant objects by EM(X,). 

The Left and Right Inductions and the Direct and Inverse Images 

Lemma 5.2. The functor ( ) j preserves arbitrary limits and colimits hence is exact) for = PA, AB, PM, Mod. 

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