Abstract
In the sense of Palamodov, a preabelian category is semi-abelian if for every morphism the natural morphism between the cokernel of its kernel and the kernel of its cokernel is simultaneously a monomorphism and an epimorphism. In this article we present several conditions which are all equivalent to semi-abelianity. First we consider left and right semi-abelian categories in the sense of Rump and establish characterizations of these notions via six equivalent properties. Then we use these properties to deduce the characterization of semi-abelianity. Finally, we investigate two examples arising in functional analysis which illustrate that the notions of right and left semi-abelian categories are distinct and in particular that such categories occur in nature.
| Original language | English |
|---|---|
| Pages (from-to) | 531-541 |
| Number of pages | 11 |
| Journal | Applied Categorical Structures |
| Volume | 20 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Oct 2012 |
| Externally published | Yes |
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Keywords
- Category of bornological spaces
- Preabelian category
- Quasi-abelian category
- Semi-abelian category
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
Cite this
On the notion of a semi-abelian category in the sense of Palamodov. / Kopylov, Yaroslav; Wegner, Sven Ake.
In: Applied Categorical Structures, Vol. 20, No. 5, 10.2012, p. 531-541.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the notion of a semi-abelian category in the sense of Palamodov
AU - Kopylov, Yaroslav
AU - Wegner, Sven Ake
PY - 2012/10
Y1 - 2012/10
N2 - In the sense of Palamodov, a preabelian category is semi-abelian if for every morphism the natural morphism between the cokernel of its kernel and the kernel of its cokernel is simultaneously a monomorphism and an epimorphism. In this article we present several conditions which are all equivalent to semi-abelianity. First we consider left and right semi-abelian categories in the sense of Rump and establish characterizations of these notions via six equivalent properties. Then we use these properties to deduce the characterization of semi-abelianity. Finally, we investigate two examples arising in functional analysis which illustrate that the notions of right and left semi-abelian categories are distinct and in particular that such categories occur in nature.
AB - In the sense of Palamodov, a preabelian category is semi-abelian if for every morphism the natural morphism between the cokernel of its kernel and the kernel of its cokernel is simultaneously a monomorphism and an epimorphism. In this article we present several conditions which are all equivalent to semi-abelianity. First we consider left and right semi-abelian categories in the sense of Rump and establish characterizations of these notions via six equivalent properties. Then we use these properties to deduce the characterization of semi-abelianity. Finally, we investigate two examples arising in functional analysis which illustrate that the notions of right and left semi-abelian categories are distinct and in particular that such categories occur in nature.
KW - Category of bornological spaces
KW - Preabelian category
KW - Quasi-abelian category
KW - Semi-abelian category
UR - http://www.scopus.com/inward/record.url?scp=84865150012&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84865150012&partnerID=8YFLogxK
U2 - 10.1007/s10485-011-9249-0
DO - 10.1007/s10485-011-9249-0
M3 - Article
VL - 20
SP - 531
EP - 541
JO - Applied Categorical Structures
JF - Applied Categorical Structures
SN - 0927-2852
IS - 5
ER -