Eck, David J. Product-preserving functors on smooth manifolds. (English) Zbl 0615.57019 J. Pure Appl. Algebra 42, 133-140 (1986). 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. Cited in 2 ReviewsCited in 14 Documents MSC: 57R99 Differential topology 18F15 Abstract manifolds and fiber bundles (category-theoretic aspects) Keywords:product preserving functors; embedding preserving functors; product- preserving natural bundle; category of connected smooth manifolds; infinitesimal neighborhoods for points × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Atiyah, M. F.; MacDonald, I. G., Introduction to Commutative Algebra (1969), Addison-Wesley: 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, (Category Theory, Homology Theory and their Applications III (1969), Springer: Springer Berlin) · Zbl 0207.53505 [5] I. Moerdijk and G.E. Reyes, \(C^∞\); I. Moerdijk and G.E. Reyes, \(C^∞\) [6] Nijenhuis, A., Natural bundles and their general properties, (Differential Geometry in Honor of K. Yano (1972), Kino Kuniya: Kino Kuniya Tokyo), 271-277 [7] Terng, C. L., Natural vector bundles and natural differential operators, Am. J. Math., 100, 4, 775-828 (1978) · Zbl 0422.58001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.