Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The homotopy theory of type theories   We construct a left semi-model structure on the category of intensional type
theories (precisely, on $\mathrm{CxlCat_{Id,1,\Sigma(,\Pi_{ext})}}$). This
presents an $\infty$-category of such type theories; we show moreover that
there is an $\infty$-functor $\mathrm{Cl}_\infty$ from there to the
$\infty$-category of suitably structured quasi-categories.
  This allows a precise formulation of the conjectures that intensional type
theory gives internal languages for higher categories, and provides a framework
and toolbox for further progress on these conjectures.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn