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Properties of well-adapted models for synthetic differential geometry. (English) Zbl 0487.18006


MSC:

18B25 Topoi
18F15 Abstract manifolds and fiber bundles (category-theoretic aspects)
51K10 Synthetic differential geometry
57P99 Generalized manifolds
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References:

[1] Dubuc, E. J., Sur les modéles de la géometrie differentielle synthetique, Cashiers Top. Géom. Differ., 20, 231-279 (1979) · Zbl 0473.18008
[2] Guillemin, V.; Pollack, A., Differential Topology (1974), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0361.57001
[3] Kock, A., A simple axiomatics for differentiation, Math. Scand., 40, 183-193 (1977) · Zbl 0375.12029
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[5] Kock, A., Formally real local rings and infinitesimal stability, Topos-Theoretic Methods in Geometry. Topos-Theoretic Methods in Geometry, Aarhus Var. Publ. Series No., 30 (1979) · Zbl 0428.03056
[6] Kock, A.; Reyes, G. E., Manifolds in formal differential geometry, Proceedings of the Durham meeting on Sheaves and Logic. Proceedings of the Durham meeting on Sheaves and Logic, Springer Lecture Notes, Vol. 753 (1977) · Zbl 0359.14015
[7] Lawvere, F. W., Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci., 50, 869-872 (1963) · Zbl 0119.25901
[8] Reyes, G. E.; Wraith, G. C., A note on tangent bundles in a category with a ring object, Math. Scand., 42, 53-63 (1978) · Zbl 0392.18011
[9] Weil, A., Théorie des points proches sur les variétés différentiables, Géometrie différentielle (1953), (Colloq. du C.N.R.S.). · Zbl 0053.24903
[10] Wraith, G. C., Generic Galois theory of local rings, Proceedings of the Durham meeting on Sheaves and Logic. Proceedings of the Durham meeting on Sheaves and Logic, Springer Lecture Notes, Vol. 753 (1977) · Zbl 0419.14013
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