Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Simplicial Nerves for Two-Dimensional Categorical Structures   The most natural notion of a simplicial nerve for a (weak) bicategory was
given by Duskin, who showed that a simplicial set is isomorphic to the nerve of
a $(2,1)$-category (i.e. a bicategory with invertible $2$-morphisms) if and
only if it is a quasicategory which has unique fillers for inner horns of
dimension $3$ and greater. Using Duskin's technique, we show how his nerve
applies to $(2,1)$-category functors, making it a fully faithful inclusion of
$(2,1)$-categories into simplicial sets. Then we consider analogues of this
extension of Duskin's result for several different two-dimensional categorical
structures, defining and analysing nerves valued in presheaf categories based
on $\Delta^2$, on Segal's category $\Gamma$, and Joyal's category $\Theta_2$.
In each case, our nerves yield exactly those presheaves meeting a certain
"horn-filling" condition, with unique fillers for high-dimensional horns.
Generalizing our definitions to higher dimensions and relaxing this uniqueness
condition, we get proposed models for several different kinds
higher-categorical structures, with each of these models closely analogous to
quasicategories. Of particular interest, we conjecture that our "inner-Kan
$\Gamma$-sets'' are a combinatorial model for symmetric monoidal
$(\infty,0)$-categories, i.e. $E_\infty$-spaces.
  This is a version of the author's Ph.D. dissertation, completed 2013 at the
University of California, Berkeley. Minor corrections and changes are included.

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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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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: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex