A universal construction in Goursat categories

Marino Gran; Diana Rodelo

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2008)

  • Volume: 49, Issue: 3, page 196-208
  • ISSN: 1245-530X

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Gran, Marino, and Rodelo, Diana. "A universal construction in Goursat categories." Cahiers de Topologie et Géométrie Différentielle Catégoriques 49.3 (2008): 196-208. <http://eudml.org/doc/91736>.

@article{Gran2008,
author = {Gran, Marino, Rodelo, Diana},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {Goursat category; Mal'cev category; reflective graph; universal groupoid},
language = {eng},
number = {3},
pages = {196-208},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {A universal construction in Goursat categories},
url = {http://eudml.org/doc/91736},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Gran, Marino
AU - Rodelo, Diana
TI - A universal construction in Goursat categories
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2008
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 49
IS - 3
SP - 196
EP - 208
LA - eng
KW - Goursat category; Mal'cev category; reflective graph; universal groupoid
UR - http://eudml.org/doc/91736
ER -

References

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  1. [1] M. Barr, Exact categories, in: Lecture Notes in Math. 236, Springer (1971), pp. 1-120. Zbl0223.18010
  2. [2] F. Borceux and D. Bourn, Mal'cev, Protomodular, Homological and Semi-Abelian categories, Math. Appl. 566, Kluwer Academic Publisher, 2004. Zbl1061.18001MR2044291
  3. [3] F. Borceux, M. Gran and S. Mantovani, On closure operators and reflections in Goursat categories, math.CT/0712.0890, vl, accepted for publication in Rend. Istit. Mat. Univ. Trieste. Zbl1153.18003MR2441612
  4. [4] D. Bourn, The denormalized 3 x 3 lemma, J. Pure Appl. Algebra, 177, 2003, 113-129. Zbl1032.18007MR1954329
  5. [5] D. Bourn and M. Gran, Categorical aspects of modularity, in Galois theory, Hopf Algebras and Semiabelian categories, G. Janelidze, B. Pareigis and W. Tholen, eds., Fields Institute Communications, 43, Amer. Math. Soc., 2004. Zbl1081.08011MR2072674
  6. [6] D. Bourn and M. Gran, Normal sections and direct product decompositions, Commun. Algebra, 32, 10, 2004, 3825-3842. Zbl1062.18003MR2097431
  7. [7] A. Carboni, G.M. Kelly and M.C. Pedicchio, Some remarks on Maltsev and Goursat categories, Appl. Categorical Structures, 1, 1993, 385-421. Zbl0799.18002MR1268510
  8. [8] A. Carboni, J. Lambek and M.C. Pedicchio, Diagram chasing in Mal'cev categories, J. Pure Appl. Algebra, 69, 1990, 271-284. Zbl0722.18005MR1090744
  9. [9] A. Carboni, M.C. Pedicchio and N. Pirovano, Internal graphs and internal groupoids in Mal'cev categories, Proc. Conference Montreal 1991, 1992, 97-109. Zbl0791.18005MR1192142
  10. [10] M. Gran, Internal categories in Mal'cev categories, J. Pure Appl. Algebra, 143, 1999, 221-229. Zbl0937.18006MR1731043
  11. [11] H.P. Gumm, Geometrical methods in congruence modular algebras, Mem. Amer. Math. Soc., 45 286, 1983. Zbl0547.08006MR714648
  12. [12] S. Lack, The 3-by-3 Lemma for regular Goursat categories, Homology, Homotopy and Applications, vol. 6 (1), 2004, 1-3. Zbl1070.18007MR2061563
  13. [13] M.C. Pedicchio, A categorical approach to commutator theory, J. Algebra 177, 1995, 647-657. Zbl0843.08004MR1358478

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