Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stratified noncommutative geometry   We introduce a theory of stratifications of noncommutative stacks (i.e.
presentable stable $\infty$-categories), and we prove a reconstruction theorem
that expresses them in terms of their strata and gluing data. This
reconstruction theorem is compatible with symmetric monoidal structures, and
with more general operadic structures such as $E_n$-monoidal structures. We
also provide a suite of fundamental operations for constructing new
stratifications from old ones: restriction, pullback, quotient, pushforward,
and refinement. Moreover, we establish a dual form of reconstruction; this is
closely related to Verdier duality and reflection functors, and gives a
categorification of M\"obius inversion.
  Our main application is to equivariant stable homotopy theory: for any
compact Lie group $G$, we give a symmetric monoidal stratification of genuine
$G$-spectra. In the case that $G$ is finite, this expresses genuine $G$-spectra
in terms of their geometric fixedpoints (as homotopy-equivariant spectra) and
gluing data therebetween (which are given by proper Tate constructions).
  We also prove an adelic reconstruction theorem; this applies not just to
ordinary schemes but in the more general context of tensor-triangular geometry,
where we obtain a symmetric monoidal stratification over the Balmer spectrum.
We discuss the particular example of chromatic homotopy theory.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph