| Title:
|
On pure quotients and pure subobjects (English) |
| Author:
|
Adámek, J. |
| Author:
|
Rosický, J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
623-636 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients. (English) |
| Keyword:
|
pure quotient |
| Keyword:
|
pure subobject |
| Keyword:
|
locally presentable category |
| Keyword:
|
semi-abelian category |
| Keyword:
|
abelian category |
| MSC:
|
18A99 |
| MSC:
|
18E99 |
| idZBL:
|
Zbl 1080.18500 |
| idMR:
|
MR2086721 |
| . |
| Date available:
|
2009-09-24T11:16:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127916 |
| . |
| Reference:
|
[1] J. Adámek and J. Rosický: Locally Presentable and Accessible Categories.Cambridge Univ. Press, Cambridge, 1994. MR 1294136 |
| Reference:
|
[2] D. Bourn: Normal subobjects and abelian objects in protomodular categories.J. Algebra 228 (2000), 143–164. Zbl 0969.18008, MR 1760960, 10.1006/jabr.1999.8249 |
| Reference:
|
[3] S. Fakir: Objects algébraiquement clos et injectifs dans les catégories localement présentables.Bull. Soc. Math. France 42 (1975). MR 0401879 |
| Reference:
|
[4] G. Janelidze, S. Márki and W. Tholen: Semi-abelian categories.168 (2002), 367–386. MR 1887164 |
| Reference:
|
[5] C. Lair: Catégories modélables et catégories esquissables.Diagrammes (1981), 1–20. Zbl 0522.18008, MR 0684749 |
| Reference:
|
[6] M. Makkai and R. Paré: Accessible categories: The foundations of categorical model theory.Contemp. Math. Vol. 104, Amer. Math. Soc., Providence, 1989. MR 1031717, 10.1090/conm/104 |
| Reference:
|
[7] P. Rothmaler: Purity in model theory.In: Advances in Algebra and Model Theory, M. Droste and R. Göbel (eds.), Gordon and Breach, , 1997, pp. 445–469. Zbl 0931.03055, MR 1687736 |
| . |
