Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An homotopical description of small presheaves   This article describes the cocompletion of a category $C$ with finite limits
as the homotopy category of some equivalence 2-groupoids in coproducts of
elements of $C$. This yields a simple link between several definitions of an
infinitary pretopos.

16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc