Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reynolds Operator on functors   Let $G= {\rm Spec} A$ 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 ${\mathcal
A}^*$-modules. We prove that $G$ is invariant exact if and only if $A^*= R
\times B^*$ as $R$-algebras and the first projection $A^* \to R$ is the unit of
$A$. If $\mathbb M$ is a dual functor of $G$-modules and $w_G := (1,0) \in R
\times B^* = A^*$, we prove that $\mathbb M^G = w_G \cdot \mathbb M$ and
$\mathbb F = w_G \cdot \mathbb M \oplus (1-w_G) \cdot \mathbb M$; hence, the
Reynolds operator can defined on $\mathcal M$.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th