Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calculating with topological Andr\'e-Quillen theory, I: Homotopical
  properties of universal derivations and free commutative $S$-algebras   We adopt the viewpoint that topological And\'e-Quillen theory for commutative
$S$-algebras should provide usable (co)homology theories for doing calculations
in the sense traditional within Algebraic Topology. Our main emphasis is on
homotopical properties of universal derivations, especially their behaviour in
multiplicative homology theories. There are algebraic derivation properties,
but also deeper properties arising from the homotopical structure of the free
algebra functor $\mathbb{P}_R$ and its relationship with extended powers of
spectra. In the connective case in ordinary $\bmod{\,p}$ homology, this leads
to useful formulae involving Dyer-Lashof operations in the homology of
commutative $S$-algebras. Although many of our results could no doubt be
obtained using stabilisation, our approach seems more direct. We also discuss a
reduced free algebra functor $\tilde{\mathbb{P}}_R$.

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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph