Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosimplicial versus DG-rings: a version of the Dold-Kan correspondence   The (dual) Dold-Kan correspondence says that there is an equivalence of
categories $K:\cha\to \Ab^\Delta$ between nonnegatively graded cochain
complexes and cosimplicial abelian groups, which is inverse to the
normalization functor. We show that the restriction of $K$ to $DG$-rings can be
equipped with an associative product and that the resulting functor
$DGR^*\to\ass^\Delta$, although not itself an equivalence, does induce one at
the level of homotopy categories. The dual of this result for chain $DG$ and
simplicial rings was obtained independently by S. Schwede and B. Shipley
through different methods ({\it Equivalences of monoidal model categories}.
Algebraic and Geometric Topology 3 (2003), 287-334). Our proof is based on a
functor $Q:DGR^*\to \ass^\Delta$, naturally homotopy equivalent to $K$, which
preserves the closed model structure. It also has other interesting
applications. For example, we use $Q$ to prove a noncommutative version of the
Hochschild-Konstant-Rosenberg and Loday-Quillen theorems. Our version applies
to the cyclic module that arises from a homomorphism $R\to S$ of not
necessarily commutative rings when the coproduct $\coprod_R$ of associative
$R$-algebras is substituted for $\otimes_R$. As another application of the
properties of $Q$, we obtain a simple, braid-free description of a product on
the tensor power $S^{\otimes_R^n}$ originally defined by P. Nuss using braids
({\it Noncommutative descent and nonabelian cohomology,} K-theory {\bf 12}
(1997) 23-74.).

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph