Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Understanding higher structures through Quillen-Segal objects   If $\mathscr{M}$ is a model category and $\mathcal{U}: \mathscr{A}
\rightarrow \mathscr{M}$ is a functor, we defined a Quillen-Segal
$\mathcal{U}$-object as a weak equivalence $\mathscr{F}: s(\mathscr{F})
\xrightarrow{\sim} t(\mathscr{F})$ such that $t(\mathscr{F})=\mathcal{U}(b)$
for some $b\in \mathscr{A}$. If $\mathcal{U}$ is the nerve functor
$\mathcal{U}: \mathbf{Cat} \rightarrow \mathbf{sSet}_J$, with the Joyal model
structure on $\mathbf{sSet}$, then studying the comma category
$(\mathbf{sSet}_J \downarrow \mathcal{U})$ leads naturally to concepts, such as
Lurie's $\infty$-operad. It also gives simple examples of presentable, stable
$\infty$-category, and higher topos. If we consider the \textit{coherent nerve}
$\mathcal{U}: \mathbf{sCat}_B \rightarrow \mathbf{sSet}_J$, then the theory of
QS-objects directly connects with the program of Riehl and Verity. If we apply
our main result when $\mathcal{U}$ is the identity $Id: \mathbf{sSet}_Q
\rightarrow \mathbf{sSet}_Q$, with the Quillen model structure, the homotopy
theory of QS-objects is equivalent to that of Kan complexes and we believe that
this is an \textit{avatar} of Voevodsky's \textit{Univalence axiom}. This
equivalence holds for any combinatorial and left proper $\mathscr{M}$. This
result agrees with our intuition, since by essence the `\textit{Quillen-Segal
type}' is the \textit{Equivalence type}

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph