The Mal'tsev operation on extensions

Dominique Bourn

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2008)

  • Volume: 49, Issue: 3, page 176-195
  • ISSN: 1245-530X

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Bourn, Dominique. "The Mal'tsev operation on extensions." Cahiers de Topologie et Géométrie Différentielle Catégoriques 49.3 (2008): 176-195. <http://eudml.org/doc/91735>.

@article{Bourn2008,
author = {Bourn, Dominique},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {protomodular category; split extension classifier; Schreier-MacLane extension theorem; Mal'tsev operation},
language = {eng},
number = {3},
pages = {176-195},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {The Mal'tsev operation on extensions},
url = {http://eudml.org/doc/91735},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Bourn, Dominique
TI - The Mal'tsev operation on extensions
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2008
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 49
IS - 3
SP - 176
EP - 195
LA - eng
KW - protomodular category; split extension classifier; Schreier-MacLane extension theorem; Mal'tsev operation
UR - http://eudml.org/doc/91735
ER -

References

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  2. [2] J. Benabou, Les distributeurs, Rapport 33, 1973, Inst. de Math. Pure et Appl. Univ. Cath. Louvain la Neuve. 
  3. [3] F. Borceux and D. Bourn, Mal'tsev, protomodular, homological and semi-abelian categories, Mathematics and Its Applications 566, Kluwer 2004. Zbl1061.18001MR2044291
  4. [4] F. Borceux, D. Bourn and P.T. Johnstone, Initial normal covers in bi-Heyting toposes, Archivum Mathematicum, 42, 2006, 335-356. Zbl1164.18301MR2283017
  5. [5] F. Borceux and D. Bourn, Split extension classifier and centrality, in Categories in Algebra, Geometry and Math. Physics, Contemporary Math., 431, 2007, 85-14. Zbl1133.18002MR2342823
  6. [6] F. Borceux, G. Janelidze and G.M. Kelly, Internal object actions, Commentationes Mathematicae Universitatis Carolinae, 46, 2005, 235-255. Zbl1121.18004MR2176890
  7. [7] F. Borceux, G. Janelidze and G.M. Kelly, On the representability of actions in a semiabelian category, Th. and Applications of Categories, 14, 2005, 244-286. Zbl1103.18006MR2182676
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  9. [9] D. Bourn, Baer sums and fibered aspects of Mal'cev operations, Cahiers de Top. et Géom. Diff. Catégoriques, 40, 1999, 297-316. Zbl0988.18006MR1734248
  10. [10] D. Bourn, Baer sums in homological categories, Journal of Algebra, 308, 2007, 414-443. Zbl1134.18004MR2290929
  11. [11] D. Bourn, Commutator theory, action groupoids, and an intrisic Schreier-Mac Lane extension theorem, Advances in Math., in press. Zbl1151.18016
  12. [12] D. Bourn and M. Gran, Centrality and normality in protomodular categories, Th. and Applications of Categories, 9, 2002, 151-165. Zbl1004.18004MR1897814
  13. [13] A. Carboni, M.C. Pedicchio and N. Pirovano, Internal graphs and internal groupoids in Mal'cev categories, CMS Conference Proceedings, 13, 1992, 97-109. Zbl0791.18005MR1192142
  14. [14] G. Janelidze, L. Marki and W. Tholen, Semi-abelian categories, Journal of Pure and Applied Algebra, 168, 2002, 367-386. Zbl0993.18008MR1887164
  15. [15] P.T. Johnstone, Affine categories and naturally Mal'cev categories, Journal of Pure and Applied Algebra, 61, 1989, 251-256. Zbl0683.18007MR1027744
  16. [16] S. Mac Lane, Homology, Springer, 1963. Zbl0818.18001MR156879
  17. [17] A. I. Mal'cev, On the general theory of algebraic systems, Mat. Sbornik N. S., 35, 1954, 3-20. Zbl0057.02403MR65533
  18. [18] O. Schreier, Uber die Erweiterungen von Gruppen, I, Monatsh. Math. u. Phys., 34, 1926, 165-180. Zbl52.0113.04MR1549403JFM52.0113.04

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