Smooth sets of fields: A pedagogical introduction

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.

Originally published in Geometric Mechanics vol. 02 no. 03, current version amended with additional references to works of Schreiber and Sati