Models of differential algebra in the context of synthetic differential geometry

Marta Bunge

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1981)

  • Volume: 22, Issue: 1, page 31-44
  • ISSN: 1245-530X

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Bunge, Marta. "Models of differential algebra in the context of synthetic differential geometry." Cahiers de Topologie et Géométrie Différentielle Catégoriques 22.1 (1981): 31-44. <http://eudml.org/doc/91249>.

@article{Bunge1981,
author = {Bunge, Marta},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {differential algebra; synthetic differential geometry; differential local ring; finitary differential ring; topos},
language = {eng},
number = {1},
pages = {31-44},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Models of differential algebra in the context of synthetic differential geometry},
url = {http://eudml.org/doc/91249},
volume = {22},
year = {1981},
}

TY - JOUR
AU - Bunge, Marta
TI - Models of differential algebra in the context of synthetic differential geometry
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1981
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 22
IS - 1
SP - 31
EP - 44
LA - eng
KW - differential algebra; synthetic differential geometry; differential local ring; finitary differential ring; topos
UR - http://eudml.org/doc/91249
ER -

References

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  1. 1 N. Bourbaki, Commutative Algebra, Hermann, Paris, 1972. MR360549
  2. 2 M. Bunge, Sheaves and prime model extensions, J. Algebra ( to appear). Zbl0465.03016MR604295
  3. 3 M.F. Coste & M. Coste, The generic model of an ε-stable geometric extension of the theory of rings is of line type, in [8], 29-36. Zbl0427.18008
  4. 4 E.J. Dubuc & G.E. Reyes, Subtoposes of the ring classifier, in [8], 101-122. Zbl0403.18003MR552659
  5. 5 C. Ehresmann, Les prolongements d'une variété différentiable, I: Calcul des jets, prolongement principal, C. R. A. S, Paris233 (1951), 598-600. Zbl0043.17401MR44198
  6. 6 A. Kock, Taylor series calculus for ring objects of line type, J. Pure and App. Algebra12 (1978), 271-293. Zbl0394.14003MR501073
  7. 7 A. Kock, On algebraic theories of power series, Cahiers Topo. et Géom. Diff. XVI-3 (1975), 266- 270. Zbl0357.13011
  8. 8 A. KOCK ( editor ), Topos theoretic methods in Geometry, Various Publications Series n° 30, Mat. Inst. Aarhus University, 1979. Zbl0396.00004MR552655
  9. 9 A. Kock, Formal manifolds and synthetic theory of jet bundles, Cahiers Topo. et Géom. Diff.XXI- 3 (1980), 227 - 241. ( Preprint Aarhus Univ.1979. ) Zbl0434.18012MR591385
  10. 10 E.R. Kolchin, Differential Algebra and algebraic groups, Academic Press, New York and London, 1973. Zbl0264.12102MR568864
  11. 11 F.W. Lawvere, Categorical Dynamics, in [8], 1-28. Zbl0403.18005MR552656
  12. 12 M. Makkai & G.E. Reyes, First order categorical Logic, Lecture Notes in Math.611, Springer (1977). Zbl0357.18002MR505486
  13. 13 J.F. Ritt, Differential Algebra, Amer. Math. Soc. Colloq. Publ.33, A. M. S., New York, 1950. Zbl0037.18402
  14. 14 A. Robinson, Introduction to model theory and to the Metamathematics of Algebra, North-Holland Pub. C°Amsterdam, 1963. Zbl0118.25302MR153570

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