Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of sheaves on algebraic stacks   Raynaud--Gruson characterized flat and pure morphisms between affine schemes
in terms of projective modules. We give a similar characterization for
non-affine morphisms. As an application, we show that every quasi-coherent
sheaf is the union of its finitely generated quasi-coherent subsheaves on any
quasi-compact and quasi-separated algebraic stack.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat