Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morita homotopy theory for $(\infty,1)$-categories and $\infty$-operads   We prove the existence of Morita model structures on the categories of small
simplicial categories, simplicial sets, simplicial operads and dendroidal sets,
modelling the Morita homotopy theory of $(\infty,1)$-categories and
$\infty$-operads. We give a characterization of the weak equivalences in terms
of simplicial presheaves, simplicial algebras and slice categories. In the case
of the Morita model structure for simplicial categories and simplicial operads,
we also show that each of these model structures can be obtained as an explicit
left Bousfield localization of the Bergner model structure on simplicial
categories and the Cisinski--Moerdijk model structure on simplicial operads,
respectively.

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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: econ