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Product-preserving functors on smooth manifolds. (English) Zbl 0615.57019

Functors from the category of connected smooth manifolds to itself which preserve products and embeddings are classified, along with natural transformations between them. Such functors that are also natural bundles can be thought of as ways of defining infinitesimal neighborhoods for points in all smooth manifolds.

MSC:

57R99 Differential topology
18F15 Abstract manifolds and fiber bundles (category-theoretic aspects)
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[1] Atiyah, M.F.; MacDonald, I.G., Introduction to commutative algebra, (1969), Addison-Wesley Reading, MA · Zbl 0175.03601
[2] Eck, D.J., Gauge-natural bundles and generalized gauge theories, Mem. am. math. soc., 247, (1981) · Zbl 0493.53052
[3] Eck, D.J., Invariants of k-jet actions, Houston J. math., 10, 2, 159-168, (1984) · Zbl 0568.14007
[4] Epstein, D.B.A., Natural vector bundles, () · Zbl 0207.53505
[5] I. Moerdijk and G.E. Reyes, C∞-rings, Preprint, Université de Montréal.
[6] Nijenhuis, A., Natural bundles and their general properties, (), 271-277
[7] Terng, C.L., Natural vector bundles and natural differential operators, Am. J. math., 100, 4, 775-828, (1978) · Zbl 0422.58001
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