Smooth sets of fields: A pedagogical introduction
Mathematical Physics
2025-10-24 v1 math.MP
Abstract
In order to provide a good categorical setting to the many different spaces of fields arising in the description of physical theories, a pedagogical introduction to the categorical notion of smooth sets is provided and some simple properties of the topos of smooth sets are discussed. The introduction of geometrical structures into such spaces is illustrated via the specific examples of the tangent functor and the variational bicomplex.
Keywords
Cite
@article{arxiv.2510.20422,
title = {Smooth sets of fields: A pedagogical introduction},
author = {Alberto Ibort and Arnau Mas},
journal= {arXiv preprint arXiv:2510.20422},
year = {2025}
}
Comments
Originally published in Geometric Mechanics vol. 02 no. 03, current version amended with additional references to works of Schreiber and Sati