Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived categories of functors and Fourier--Mukai transform for quiver
  sheaves   Let C be small category and A an arbitrary category. Consider the category
C(A) whose objects are functors from C to A, and whose morphisms are natural
transformations. Given a functor F : A --> B one obtains an induced functor F_C
: C(A) --> C(B) . If A and B are abelian categories, we have that C(A) and C(B)
are also abelian, and one has two functors R(F_C) : D(C(A)) --> D(C(B)) and
(RF)_ C : C(D(A)) --> C(D (B)). The goals of this paper are: 1) to find a
relationship between D (C(A)) and C(D(A)); 2) to relate the functors R(F_C) and
(RF)_C. As an application, we prove a version of Mukai's Theorem for quiver
sheaves.

12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin