Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Category-Theoretic Reconstruction of Schemes from Categories of Reduced
  Schemes   Let $S$ be a locally Noetherian normal scheme and $\blacklozenge/S$ a set of
properties of $S$-schemes. Then we shall write Sch$_{\blacklozenge/S}$ for the
full subcategory of the category of $S$-schemes Sch$_{/S}$ determined by the
objects $X\in {\rm Sch}_{\blacklozenge/S}$ that satisfy every property of
$\blacklozenge/S$. In the present paper, we shall mainly be concerned with the
properties "reduced", "quasi-compact over $S$", "quasi-separated over $S$", and
"separated over $S$". We give a functorial category-theoretic algorithm for
reconstructing $S$ from the intrinsic structure of the abstract category
Sch$_{\blacklozenge/S}$. This result is analogous to a result of Mochizuki
\cite{Mzk04} and may be regarded as a partial generalization of a result of de
Bruyn \cite{deBr19} in the case where $S$ is a locally Noetherian normal
scheme.

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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
9
The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: hep-ph