User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

A new characterisation of Goursat categories

Primary tabs

Gran, Marino [UCL] Rodelo, Diana [Univ. of Algarve, Math. Dept.]

We present a new characterisation of Goursat categories in terms of special kind of pushouts, that we call Goursat pushouts. This allows one to prove that, for a regular category, the Goursat property is actually equivalent to the validity of the denormalised 3-by-3 Lemma. Goursat pushouts are also useful to clarify, from a categorical perspective, the existence of the quaternary operations characterising 3-permutable varieties.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2012
Language Anglais
Journal information "Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science" - Vol. 20, no. 3, p. 229-238 (2012)
Peer reviewed yes
Publisher Springer Netherlands ((Netherlands) Dordrecht)
issn 0927-2852
Publication status Publié
Affiliations UCL - SST/IRMP - Institut de recherche en mathématique et physique
Univ. of Algarve, Math. Dept. - SST/IRMP
Links
  1. Borceux, F., Bourn, D.: Mal’cev, Protomodular, Homological and Semi-Abelian Categories. Kluwer (2004)
  2. Borceux, F., Gran, M., Mantovani, S.: On closure operators and reflections in Goursat categories. Rend. Ist. Mat. Trieste 39, 87–104 (2007)
  3. Bourn Dominique, The denormalized 3×3 lemma, 10.1016/s0022-4049(02)00143-3
  4. Carboni A., Kelly G. M., Pedicchio M. C., Some remarks on Maltsev and Goursat categories, 10.1007/bf00872942
  5. Carboni A., Lambek J., Pedicchio M.C., Diagram chasing in Mal'cev categories, 10.1016/0022-4049(91)90022-t
  6. Carboni, A., Pedicchio, M.C.: A new proof of the Mal’cev theorem. Rend. Circ. Mat. Palermo, S. II, Suppl. 64, 13–16 (2000)
  7. Gran, M., Rodelo, D.: A universal construction in Goursat categories. Cah. Topol. Géom. Différ. Catég. XLIX-3, 196–208 (2008)
  8. Gran, M., Pedicchio, M.C.: n-permutable locally finitely presentable categories. Th. Appl. Categ. 8(1), 1–15 (2001)
  9. Hagemann J., Mitschke A., Onn-permutable congruences, 10.1007/bf02945100
  10. Janelidze G., Kelly G.M., Galois theory and a general notion of central extension, 10.1016/0022-4049(94)90057-4
  11. Janelidze, G., Sobral, M.: Descent for regular epimorphisms in barr exact Goursat categories. Appl. Categ. Struct. doi: 10.1007/s10485-009-9199-y
  12. Janelidze Zurab, Subtractive Categories, 10.1007/s10485-005-0934-8
  13. Janelidze, Z.: The pointed subobject functor, 3 ×3 lemmas, and subtractivity of spans. Th. Appl. Categ. 23(11), 221–242 (2010)
  14. Lack Stephen, The 3-by-3 lemma for regular Goursat categories, 10.4310/hha.2004.v6.n1.a1
  15. Mitschke Aleit, Implication algebras are 3-permutable and 3-distributive, 10.1007/bf02944976
  16. Rossi Valentina, Admissible Galois Structures and Coverings in Regular Mal’cev Categories, 10.1007/s10485-006-9026-7
Bibliographic reference Gran, Marino ; Rodelo, Diana. A new characterisation of Goursat categories. In: Applied Categorical Structures : a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science, Vol. 20, no. 3, p. 229-238 (2012)
Permanent URL http://hdl.handle.net/2078.1/108292