Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pretorsion theories in general categories   We present a setting for the study of torsion theories in general categories.
The idea is to associate, with any pair ($\mathcal T$, $\mathcal F$) of full
replete subcategories in a category $\mathcal C$, the corresponding full
subcategory $\mathcal Z = \mathcal T \cap \mathcal F$ of \emph{trivial objects}
in $\mathcal C$. The morphisms which factor through $\mathcal Z$ are called
$\mathcal Z$-trivial, and these form an ideal of morphisms, with respect to
which one can define $\mathcal Z$-prekernels, $\mathcal Z$-precokernels, and
short $\mathcal Z$-preexact sequences. This naturally leads to the notion of
pretorsion theory, which is the object of study of this article, and includes
the classical one in the abelian context when $\mathcal Z$ is reduced to the
$0$-object of $\mathcal C$. We study the basic properties of pretorsion
theories, and examine some new examples in the category of all endomappings of
finite sets and in the category of preordered sets.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs