Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Higher Coalgebra   We define quasicategories of E_n-structured coalgebras, bialagebras and
comodules. We show that: n-fold loop spaces, suspension spectra thereof,
descent data for maps of E_n-ring spectra, descent corings of morphisms of
E_n-ring spectra and Thom spectra are all examples of these kinds of objects.
In particular, we prove that for a morphism of E_n-monoidal Kan complexes
f:X->BGL_1(R), the associated Thom spectrum Mf is a structured R[X]-comodule by
the classical Thom diagonal.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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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: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex