Reynolds Operator on Functors
نویسندگان
چکیده
Let G = SpecA be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗ = R × B∗ as R-algebras and the first projection A∗ → R is the unit of A. If M is a dual functor of G-modules and wG := (1, 0) ∈ R×B ∗ = A∗, we prove that M = wG ·M and M = wG · M ⊕ (1 − wG) · M; hence, the Reynolds operator can be defined on M.
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