On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 28 (1987) no. 2, pp. 127-142.
@article{CTGDC_1987__28_2_127_0,
     author = {Bunge, Marta},
     title = {On a synthetic proof of the {Ambrose-Palais-Singer} theorem for infinitesimally linear spaces},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {127--142},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {28},
     number = {2},
     year = {1987},
     mrnumber = {913968},
     zbl = {0628.18005},
     language = {en},
     url = {http://archive.numdam.org/item/CTGDC_1987__28_2_127_0/}
}
TY  - JOUR
AU  - Bunge, Marta
TI  - On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces
JO  - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY  - 1987
SP  - 127
EP  - 142
VL  - 28
IS  - 2
PB  - Dunod éditeur, publié avec le concours du CNRS
UR  - http://archive.numdam.org/item/CTGDC_1987__28_2_127_0/
LA  - en
ID  - CTGDC_1987__28_2_127_0
ER  - 
%0 Journal Article
%A Bunge, Marta
%T On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces
%J Cahiers de Topologie et Géométrie Différentielle Catégoriques
%D 1987
%P 127-142
%V 28
%N 2
%I Dunod éditeur, publié avec le concours du CNRS
%U http://archive.numdam.org/item/CTGDC_1987__28_2_127_0/
%G en
%F CTGDC_1987__28_2_127_0
Bunge, Marta. On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 28 (1987) no. 2, pp. 127-142. http://archive.numdam.org/item/CTGDC_1987__28_2_127_0/

1, W. Ambrose, R.S. Palais & I.M. Singer, Sprays, Anais da Acad, Bras, de Ciencias, 32-2 (1960). 163-178. | MR | Zbl

2, F. Bergeron, Objets infinitésimalement linéaires dans un modèle bien adapté de G. D.S., in; Géométrie Différenteille Synthétique, Ed, G, E, Reyes, Rapport des recherches DMS 80-12, Univ, Montréal, 1980,

3, M. Bunge & E. Dubuc, Local concepts in SDG and germ representability, In: Mathematical Logic and Theoretic Computer Science, Eds, E, G, K, Lopez Escobar & al., Marcel Dekker Inc., New York, 1987, 93-159, | MR | Zbl

4, M. Bunge & M. Heggie, Synthetic Calculus of variations, in: Mathematical applications of Category theory, Ed, J, W, Gray, Contemporary Math, vol, 30, A, M, S, 1984, 30-62, | MR | Zbl

5, M. Bunge & P. Sawyer, On connections, geodesics and sprays in SDG, Cahiers Top, et Géom, Diff, Categ, XXV-3 (1984), 221-257, | Numdam | MR | Zbl

6, C. Ehresmann, Les prolongements d'une variété différentiable, I, II, III, C, R, A, S Paris 1951; reprinted in Charles Ehresmann: Oeuvres complètes et commentées, Part I, Amiens, 1984,

7, C. Godbillon, Géométrie Différentielle et Mécanique Analytique, Hermann, Paris, 1969, | MR | Zbl

8, P.T. Johnstone, Topos Theory, London Math, Soc, Monograph 10, Academic Press, 1977, | MR | Zbl

9, A. Kock & G.E. Reyes, Connections in formal Differential geometry, Aarhus Math, Inst, Var, Pub, Series 30 (1979), | MR | Zbl

10, A., Kock, Synthetic Differential Geometry, Cambridge University Press, 1981, | MR | Zbl

11, A. Kock, Remarks on connections and sprays, in: Category theoretic methods in Geometry, Aarhus Math, Inst, Var, Pub, Series 35 (1983), | MR | Zbl

12, A. Kock & R. Lavendhomme, Strong infinitesimal linearity, with applications to strong difference and affine connections, Cahiers Top, et Géom, Diff, Categ, XXV-3 (1984), 311-324, | Numdam | MR | Zbl

13, S., Maclane, Categories for the working mathematician, Graduate texts in Math, 5, Springer, 1971, | MR | Zbl

14, S., Lang, Introduction to differentiable manifolds, Interscience, 1962, | MR | Zbl

15, F.W. Lawvere, Categorical Dynamics, Aarhus Math, Inst, Var, Pub, Series 30 (1979), 1-29, | MR | Zbl

16, I. Moerdijk & G.E. Reyes, Connections on microlinear spaces, Rapport des recherches, DMS 85-3, Univ, de Montréal (1985),

17, I. Moerdijk & G.E. Reyes, On the relation between connections and sprays, Univer, of Amsterdam, Math, Inst, Report 85-18 (1985),

18, L.N. Patterson, Connections and prolongations, Can, J Math, XXVII-4 (1975), | MR

19, W.A. Poor, Differential geometrie structures, McGraw Hill, 1981, | MR | Zbl

20, B. Veit-Riccioli, Structures on iterated tangent bundles, manuscript, 1981,

21, A. Weil, Théorie des points proches sur les variétés différentiables, Coll, Inter, Top, et Géom Diff, Strasbourg, C, N, R, S, (1953), | MR | Zbl