Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-localizations of semi-abelian categories   A semi-localization of a category is a full reflective subcategory with the
property that the reflector is semi-left-exact. In this article we first
determine an abstract characterization of the categories which are
semi-localizations of an exact Mal'tsev category, by specializing a result due
to S. Mantovani. We then turn our attention to semi-abelian categories, where a
special type of semi-localizations are known to coincide with torsion-free
subcategories. A new characterisation of protomodular categories in terms of
binary relations is obtained, inspired by the one discovered in the pointed
context by Z. Janelidze. This result is useful to obtain an abstract
characterization of the torsion-free and of the hereditarily-torsion-free
subcategories of semi-abelian categories. Some examples are considered in
detail in the categories of groups, crossed modules, commutative rings and
topological groups. We finally explain how these results extend similar ones
obtained by W. Rump in the abelian context.

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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom