Tim de Laat's bachelor thesis might be of interest:
Synthetic Differential Geometry: An application to Einstein’s Equivalence Principle
This thesis is the result of my bachelor project in both Mathematics and Physics & Astronomy. The aim of this project was to give a satisfactory and rigorous formulation of the equivalence principle of the general theory of relativity (gr) in terms of synthetic differential geometry (sdg). sdg is a “natural” formulation of differential geometry in which the notion of “infinitesimals” is very important. Smooth infinitesimal analysis (sia) is the mathematical analysis corresponding to these infinitesimals and it forms an entrance to sdg. Both sia and sdg are formulated in terms of categories and topoi. As I was quite new to these subjects, I first needed to study them thoroughly before I could start studying sdg