Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Internal and local homotopy theory   There is a well-established homotopy theory of simplicial objects in a
Grothendieck topos, and folklore says that the weak equivalences are
axiomatisable in the geometric fragment of $L_{\omega_1, \omega}$. We show that
it is in fact a theory of presheaf type, i.e. classified by a presheaf topos.
As a corollary, we obtain a new proof of the fact that the local Kan fibrations
of simplicial presheaves that are local weak homotopy equivalences are
precisely the morphisms with the expected local lifting property.

24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat