Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial monads and delooping of mapping spaces   We extend some classical results - such as Quillen's Theorem A, the
Grothendieck construction, Thomason's Theorem and the characterisation of
homotopically cofinal functors - from the homotopy theory of small categories
to polynomial monads and their algebras.
  As an application we give a categorical proof of the Dwyer-Hess and Turchin
results concerning the explicit double delooping of spaces of long knots.

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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-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: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org