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Fibered Manifolds, Natural Bundles, Structured Sets, G-Sets and all that: The Hole Story from Space Time to Elementary Particles

J. Stachel·M. Iftime
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Abstract

In this paper we review the hole argument for the space-time points and elementary particles and generalize the hole argument to include all geometric object fields and diffeomorphisms; and, by application of forgetful functors to abstract from differentiability and even continuity, the hole argument is applied to a much wider class of mathematical objects. We discuss the problem concerning the individuation of the objects in more general settings such that fibered manifolds, fibered sets and n-ary relations.

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J. Stachel, M. Iftime. 2005-05-28. Fibered Manifolds, Natural Bundles, Structured Sets, G-Sets and all that: The Hole Story from Space Time to Elementary Particles. https://arxiv.org/abs/gr-qc/0505138

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