Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dual Representation in Spectral Algebraic Geometry   Given a spectral Deligne-Mumford stack $X$, we define a perception of $X$ to
be a collection of a certain class of morphisms $Y \rightarrow X$. For the
class of affine morphisms in SpDM, we show that from QCoh($X$) on can extract
the affine perception $\text{Aff}_X$ of $X$ on the one hand, and a subcategory
of an $\infty$-category of representations $\text{Rep}_{\mathfrak{g}_*}$ of a
dg Lie algebra $\mathfrak{g}_*$ associated with $X$ on the other. For the class
of local morphisms $\text{Sp\'et } R \rightarrow X$, the local perception of
$X$ is given by the functor $\mathbf{X} = \text{Hom}(\text{Sp\'et}(-), X)$ it
represents. If $\mathbf{X}$ is a geometric stack, Tannaka duality allows us to
recover $\mathbf{X}$ from $\text{QCoh}(\mathbf{X})$, from which we can also
get, after base change, a subcategory of $\text{Rep}_{\mathfrak{g}_*}$. We
generalize those results by considering functors $\mathbf{X}:
\text{CAlg}^{\text{cn}} \rightarrow \mathcal{S}$ that are representable in
accordance with the spectral Artin representability theorem of Lurie.

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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th