On the characterization of Jonsson-Tarski and of subtractive varieties

Marino Gran; Diana Rodelo

Diagrammes (2012)

  • Volume: 67-68, page 101-115
  • ISSN: 0224-3911

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Gran, Marino, and Rodelo, Diana. "On the characterization of Jonsson-Tarski and of subtractive varieties." Diagrammes 67-68 (2012): 101-115. <http://eudml.org/doc/272970>.

@article{Gran2012,
author = {Gran, Marino, Rodelo, Diana},
journal = {Diagrammes},
keywords = {abelian categories; exact categories; algebraic theories; projective covers; varieties of universal algebras; regular categories; subtractive varieties; Jónsson-Tarski varieties},
language = {eng},
pages = {101-115},
publisher = {Université Paris 7, Unité d'enseignement et de recherche de mathématiques},
title = {On the characterization of Jonsson-Tarski and of subtractive varieties},
url = {http://eudml.org/doc/272970},
volume = {67-68},
year = {2012},
}

TY - JOUR
AU - Gran, Marino
AU - Rodelo, Diana
TI - On the characterization of Jonsson-Tarski and of subtractive varieties
JO - Diagrammes
PY - 2012
PB - Université Paris 7, Unité d'enseignement et de recherche de mathématiques
VL - 67-68
SP - 101
EP - 115
LA - eng
KW - abelian categories; exact categories; algebraic theories; projective covers; varieties of universal algebras; regular categories; subtractive varieties; Jónsson-Tarski varieties
UR - http://eudml.org/doc/272970
ER -

References

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  1. [1] J. Adamek and H. Porst, Algebraic theories of quasivarieties, J. Algebra, 208 (1998) 379-398. Zbl0913.18004
  2. [2] M. Adelman, Abelian categories over additive ones, J. Pure Appl. Algebra3 (1973) 103-117. Zbl0287.18009
  3. [3] M. Barr, Exact Categories, in: Lecture Notes in Math. 236, Springer (1971) 1-120. 
  4. [4] F. Borceux and D. Bourn, Mal'cev, protomodular, homological and semi-abelian categories, Kluwer, 2004. 
  5. [5] D. Bourn, Mal'cev categories and fibration of pointed objects, Appl. Categ. Structures4 (1996) 307-327. Zbl0856.18004
  6. [6] A. Carboni, J. Lambek, and M.C. Pedicchio, Diagram chasing in Malcev categories, J. Pure Appl. Algebra69 (1991) 271-284. Zbl0722.18005
  7. [7] A. Carboni and R. Celia Magno, The free exact category on a left exact one, . Austr. Math. Soc. Ser., A 33 (1982) 295-301. Zbl0504.18005
  8. [8] A. Carboni and M.C. Pedicchio, A new proof of the Mal'cev theorem, Rend. Circolo Mat. Palermo, S. II, Suppl. 64 (2000) 13-16. Zbl0966.18005
  9. [9] A. Carboni and G. Rosolini, Locally cartesian closed exact completions, J. Pure Appl. Algebra154 (2000) 103-116. Zbl0962.18001
  10. [10] A. Carboni and E. Vitale, Regular and exact completions, J. Pure Appl. Algebra125 (1998) 79-116. Zbl0891.18002
  11. [11] M. Gran, Semi-abelian exact completions, Homology, Hom. Appl.4 (2002) 175-189. 
  12. [12] M. Gran and E.M. Vitale, On the exact completion of the homotopy category, Cah. Top. Geom. Diff. CategoriquesXXXIX-4 (1998) 287-297. Zbl0918.18003
  13. [13] P. Freyd, Representations in abelian categories, in: Proc. Conference on Categorical Algebra, La Jolla, 1965 (Springer, Berlin, 1966). Zbl0202.32402
  14. [14] Z. Janelidze, Subtractive categories, Appl. Categ. Structures13 (2005) 343-350. 
  15. [15] B. Jonsson and A. Tarski, Direct Decompositions of Finite Algebraic Systems, Notre Dame Mathematical Lectures, Notre Dame, Indiana (1947) Zbl0041.34501
  16. [16] F. W. Lawvere, Functorial Semantics of Algebraic Theories, Ph.D. thesis, Columbia University (1963), Reprint in Theory and Applications of Categories5 (2004) 1-121. Zbl0119.25901
  17. [17] M. Menni, A characterization of the left exact categories whose exact completions are toposes, J. Pure Appl. Algebra177 (2003) 287-301. Zbl1050.18002
  18. [18] J. Rosicky, Cartesian closed exact completions, J. Pure Appl. Algebra142 (1999) 261-270. Zbl0937.18003
  19. [19] J. Rosicky and E.M. Vitale, Exact completions and representations in abelian categories, Homology, Hom. Appl.3 (2001) 453-466. Zbl0993.18001
  20. [20] A. Ursini, On subtractive varieties, I. Algebra Universalis31 (1994) 204-222. Zbl0799.08010
  21. [21] E. Vitale, Left covering functors, PhD thesis, Université catholique de Louvain (1994) 

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