Rational torus-equivariant stable homotopy II: Algebra of the standard model

For any torus G=S1×⋯×S1, the author has introduced [2], a category A(G) and together with Shipley has shown that [3] it provides an algebraic model for rational G-equivariant cohomology theories. This paper studies a number of purely algebraic properties of A(G). It is shown that the category A(G) has injective dimension equal to the rank of G, flatness properties are proved and right adjoints are constructed for the inclusion of A(G) into certain larger categories, giving explicit constructions of limits in A(G).