Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dualizable and semi-flat objects in abstract module categories   In this paper, we define what it means for an object in an abstract module
category to be dualizable and we give a homological description of the direct
limit closure of the dualizable objects. Our description recovers existing
results of Govorov and Lazard, Oberst and R{\"o}hrl, and Christensen and Holm.
When applied to differential graded modules over a differential graded algebra,
our description yields that a DG-module is semi-flat if and only if it can be
obtained as a direct limit of finitely generated semi-free DG-modules. We
obtain similar results for graded modules over graded rings and for
quasi-coherent sheaves over nice schemes.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph