Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalities and Commutators   We first compare several algebraic notions of normality, from a categorical
viewpoint. Then we introduce an intrinsic description of Higgins' commutator
for ideal-determined categories, and we define a new notion of normality in
terms of this commutator. Our main result is to extend to any semi-abelian
category the following well-known characterization of normal subgroups: a
subobject $K$ is normal in $A$ if, and only if, $[A,K]\leq K$.

36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics