Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Elmendorf-Piacenza type Theorem for Actions of Monoids   Let $M$ be a monoid and $G:\mathbf{Mon} \to \mathbf{Grp}$ be the group
completion functor from monoids to groups. Given a collection $\mathcal{Z}$ of
submonoids of $M$ and for each $N\in \mathcal{Z}$ a collection $\mathcal{Y}_N$
of subgroups of $G(N)$, we construct a model structure on the category of
$M$-spaces and $M$-equivariant maps, in which weak equivalences and fibrations
are determined by the standard $\mathcal{Y}_N$-model structures on
$G(N)$-spaces for all $N\in \mathcal{Z}$. We also show that there is a small
category $\mathsf{O}_(\mathcal{Z},\mathcal{Y})$ such that, under mild
conditions on $\mathcal{Z}$ and $\mathcal{Y}_N$'s, the projective model
structure on the category of contravariant
$\mathsf{O}_(\mathcal{Z},\mathcal{Y})$-diagrams of spaces is Quillen equivalent
to our model structure. In particular, we prove a theorem generalizing
Elmendorf-Piacenza Theorem to actions of monoids.

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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph